Bombs are easily the most tactics heavy utilities.
This makes them rather niche in terms of use when paired with swords, since there are few situations you would forgo using a sword to start charging a bomb, bar slow moving monster crowd control or status distribution.

This is an unfortunate fact of bombs, using all bombs is not a viable strategy in this game, they are purely utilities.
While bombs like the Fiery Vaporizer deal excellent group DPS and normal damage bombs like the Nitronome or Irontech Destroyer can deal sword levels of damage to whole crowds, their inability to deliver instant damage to monsters like Gun Puppies makes them quite difficult to use outside of group play.
Using them with swords is more of a way to supplement their inherent weakness rather than improve your effectiveness.

For these reasons, I will only recommend a few bombs to be used in conjunction with swords:

• Venom Veiler/Shivermist Buster: Tremendously useful status distributors. They can change the tide of unfavourable fights. Venom Veilers are particular useful against pesky groups of Gremlins, while the Shivermist Buster can deliver ungodly amounts of Crowd Control. While you will rarely need both at once, having them there is usually a good idea.
• Graviton Vortex: This thing is just plain cool. Using it in Danger Rooms is also, the single greatest thing you can do with it. Especially ones with jellies. Using this in conjunction with a Venom Veiler will give you Crowd Control and Status Distribution, while simultaneously allowing you to put the hurt on jellies that like to heal via status effects. You can also combo it with Khorovod or Iron Slug to deliver big damage and stun to groups of any monster.
• Crystal Bomb: This and it's variants, the Ionized Salt Bomb and Radiant Sun Shards, are the best single target damage bombs have to offer. Lure anything on top of one of them and there's a pretty good chance it's going to die. That said, using them is difficult and in a group, it will be nigh impossible to shoot all 8 shards into one monster. Not to mention, charging anything in close proximity to any monster is just a horrible idea. The plus side is, they have Piercing Damage, which helps with Swords, since no sword deals Piercing.

Now you might be thinking, where are the Normal Damage bombs? What about the Ash of Agni?

Bombs don't interrupt attacks. This means monsters that don't get knocked back very far, like Lumbers, can still land a hit on you if you're not fast enough. Bomb damage might be fairly high, but since it's equal to one sword swing, in most cases having a bomb for damage is just for people who want to use all bombs. Swords apply damage much better, they apply it more consistently and at a close range, some of them can interrupt attacks.

As for the Ash of Agni, using it in Tier 3 just isn't recommended. Most monsters are immune to fire. Lets not forget that in some of the best places to use the Ash of Agni, like Danger Rooms and Arenas, Oilers are likely to spawn. And if you have that Ash of Agni charged up and they pop out, you just doomed yourself and your whole party. It's a risky weapon to use at this time. Basically, it's an excellent bomb, just not right now.

I don't think I really need to spell out what weapons to use, as your choices when it comes to Sword/Bomb are pretty limited.

1. Divine Avenger: Elemental/Normal. Long range charge attack.
2. Gran Faust/Graviton Bomb: Shadow damage. Choice between massive damage and curse support or awesome CC.
3. Ionized Salt Bomb/Radiant Sun Shards: Piercing damage, massive damage when used properly. Great for kiting.
4. Venom Veiler/Shivermist Buster: Status Distribution. As for which status, just pick what you hate more, getting swamped by monsters or healers.

You'll probably wear full Vog Cub or Vog Cub + Volcanic Demo with a Grey Owlite Shield/Omega Shell.
This is as good as it gets for Sword/Bomb combos.
It's not exactly a fun or exciting set, but it is what it is.

Besides, if you wanted to have fun, you wouldn't be in Tier 3, because Tier 3 is explicitly and implicitly a No Fun Zone.
Ask Magnus.

Copied from my post here: http://forums.spiralknights.com/en/node/2252#comment-13535

Just for the benefit of those who haven't read it yet.
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For close range attacks, fights in tight spaces or against monsters who randomly dodge, an Autogun type weapon can replace your sword. It doesn't stop monsters from dodging, but at close range, theres no way they can get out of the way of your bullets. I'm not sure how the Volcanic Pepperbox is in it's current incarnation, but it should still be an excellent weapon for straight up ranged DPS. Since it deals Normal Damage it's equally effective on all monsters as well. You could use the Valiance for Normal Damage, but it's very plain. Using Normal Damage isn't recommended most of the time anyway, only as a last resort. The Volcanic Pepperbox makes a much better last resort weapon than the Valiance in all situations that would require it, anyway.

For elemental attacks, you have a lot of choice. The Firotech Alchemer, Voltech Alchemer, Cryotech Alchemer and Prismatech Alchemer all deal Elemental Damage amazingly well. While the Alchemers that deal a status effect can be less desirable during certain situations, like Oilers and Quicksilvers, the Prismatech Alchemer is neutral, in that it doesn't deal a status effect. This can also be a downside, as you're using one slot purely just to deal with two kinds of enemies (Constructs and Undead). I would recommend any of them, as Shadow damage is strong against Slimes and won't set any of their special effects off by accident.

The Shadowtech Alchemer is currently the only gun in the game that deals pure Shadow Damage. The Sentenza deals Shadow and Piercing damage, which makes it less effective against Slimes (but still effective on Gremlins), however because it is so fast and spammable, some people prefer it to having two Alchemers. Although I don't recommend it.

The last gun you'll need is the Callahan, which deals pure piercing damage and has an extraordinary range. Using it from long range means monsters won't dodge your charge attack bullet, this makes it very easy to take out Wolvers and Devilites. This gun's big brother, the Iron Slug, is also an excellent gun, however it deals normal damage instead of piercing. It explodes in an area of effect on hit, making it good for controlling monsters, but it also hits stationary monsters like Gun Puppies twice on a charge attack. They both stun, which slows monsters down considerably. The only real downside is that occasionally, the charge attack can stun you as well.

There is another possible set, though.

Mainly, swapping the Volcanic Pepperbox for a Blitz Needle and having the Iron Slug for normal damage instead.
Since the Blitz Needle counters Wolver and Devilite dodging quite expertly, you can use it purely to wipe them out on sight.
Keeping the Iron Slug to execute monsters from outside of their range of attack.
Either way, it's still relatively balanced.

So the best loadout for all Guns currently is:

1. Volcanic Pepperbox: Normal Damage, High DPS weapon. Chance to inflict Fire.
2. Hail Driver: Elemental Damage. Crowd Control, monster abilities can't accidentally triggered by the Freeze Status.
3. Umbra Driver: Only gun in the game that deals pure Shadow Damage.
4. Callahan: Deals the highest Piercing Damage out of all Handguns. Extreme long range attack. Chance to stun monsters.

It gives a good balance. All monster types are covered. You get three status effects, Fire, Freeze and Stun. Every range of attack is covered, from Short to Extreme Long range. There aren't any compromises, bar the chance for stun from the Callahan. But Stun is by far the least troublesome status, since you can still block while stunned and you can cure it with a Remedy pill.

Personally, I would use:

1. Iron Slug
2. Blitz Needle
3. Sentenza
4. Storm Driver

If I were to play using all guns.
Just because those weapons all look awesome and still do an excellent job of annihilating everything in your way.
It's by no means an ideal set, but if I'm going to be playing for weeks to get weapons, I want them to at least be as cool as I am.

If I had to use only two guns...
I'd use the Sentenza and Hail Driver.
Sentenza for spamming down health and the Hail Driver for crowd control.

Your armour doesn't really matter. Guns are fairly slow, so just using a Swiftstrike Buckler with some Gun Charge Time Reduction armour or Increased Gun Damage armour will do wonders. Trinkets are even better. If you want a shield that offers better defense, you won't suffer for not having high attack speed, though.
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Guns generally do less damage, due to the fact with the right amount of kiting and positioning it's entirely possible to never be hit by an enemy.
The Cryotech Alchemer makes not getting hit even easier by freezing monsters.
Once you upgrade it you'll see that, for the most part, it is one of the best guns you can get.

As for armour, all the best bonuses for gunners only appear at 5-star.
This means that in the long run, having more defensive gear will be much more useful than leveling up useless gear that offers up terrible defenses (Gunslinger).
Which, if you were going to do so, there are really only two choices:
Deadshot and Nameless.

Although, going all Gun, while it's feasible, you would be much better off using swords like the Divine Avenger and Gran Faust if you're only going to use two slots.
There aren't any weapons better than those two in the entire game.

@Evie91: I think the Firebrand and Blizzbrand swords are quite useful weapons in their own ways, but the Nightblade is still outclassed heavily by the Faust. I would really only recommend the Nightblade if you need some cheap and easy Shadow Damage, don't want to farm Jelly King or you don't want to get gear for Attack Speed.

I also need to update that swords only section, since now there are swords that deal Piercing Damage.