Trying to play only-bomb/gun/sword, especially with only two weapon slots, is kind of asking for trouble, especially if you are solo. Although with the arsenal stations now, you can regear on almost every level- so definitely tailor your loadout depending on the level, and don't try to stick to a single weapon type all the time (unless you really want the challenge). For example, you should consider bringing a good anti-turret gun or sword to a construct themed Clockworks Tunnel level- there's a good chance you'll run into a series of turrets.

If I had to run straight bombs, I would probably choose Ash as a permanent fixture (except on fire levels; replace with VT there), followed by either DBB, Nitronome or RSS. I won't say Shivermist is for wusses (because it is the correct answer to fiends in a party, or if your party isn't very skilled/has high latency), but my preference is always more damage rather than crowd control (which can be done via good kiting). Getting a third weapon slot is definitely worth it if you play at least a few hours per week- it allows you to be enormously flexible once you have the weapons to fill various roles.