When I got the bomb I thought it would be useful to plant a bomb in front of a group of enemies so I could get a few more hits in with my sword, but the stun doesn't seem to be doing anything to them. I still get hit as if I had combo'd into a crowd of enemies without the bomb. What am I doing wrong?
Tips on using the Haze Bomb/Stagger Storm solo?
Are you fighting oilers, quiksilvers, or ice cubes? Because those three are immune to stun.
Stun slows attacks and makes them more predictable, it doesn't increase the flinch chance of monsters nor does it stop movement. Stagger Storm isn't a bomb made to let you use combos it is a bomb made to give you time to charge your weapon and help you dodge melee attacks.
The points made by everyone above are all valid. @Holy-Nightmare does a very good job in explaining what stun is. Don't get it mixed up with Freeze or Sleep, both of which will more or less prevent monsters from attacking you altogether (the former prevents them from attacking you unless you happen to be standing in front of them, the latter makes them fall asleep altogether). Certain monsters are immune to stun, as stated by @Almond Riddle. Finally, make sure monsters are within the AoE of your bomb, or else you won't be stunning anything.
The bomb is a lot like Shivermist Buster at Firestorm Citadel. It basically gives the monsters a handicap, although it is not (usually) necessary. A lot of times, if you are in a skilled party, it only serves to slow things down and cause confusion. As for your problem, I would agree with Bopp's guess. If you had taken the time to heat it to 5*, surely you would have realized these problems you are facing and either stopped crafting or found a way around them. You stated that you "still get hit as if I had combo'd into a crowd of enemies without the bomb." Stun does not stop monsters from attacking! If you are completing entire combos, chances are the monsters will attack you before you can finish. Try a different strategy, such as taking the time to charge a weapon (preferably brandish) at a distance from the crowd, releasing the attack and backing away to safety.
Ive used the Stagger Storm with a Troika line sword, and comboing the Stun with the charge is awesome.
It compensates for the slow speed when charging and blasts all of the enemies away, so that I don't have issues with attacking an enemy while it is losing the status, which is really weird considering your enemy just got an ASI boost back.
While your question is for use in solo, if in a group, I would either recommend using it 24/7 or not at all, for making your teammates have to readjust to the changing attack speeds is frustrating. This might also apply when playing by yourself.
Stagger Storm is pretty reliable and effective in my experience. Are you using the 2-star version, which has a tiny radius? Then maybe you're not actually stunning most of the monsters? That's my best guess, sorry.