Yes forget about fast shutter as some have said it's easer than it looks set camera to bulb . Pre focus the area in daylight . Or anything in the that you can use smaller fstop . When something is going hit shutter and count of seconds one thousand one , one thousand two etc . Leave shutter open tell you think you have some good ones .some times I take a three second or more shot throw a hat over the len's move the camera where you think you
Have a blank spot , take the hat away if you see one in that spot count a few sec then close shutter . And they look better if your a fair way back don't zoom in on them unless you want to cover one ot two booms in the whole frame . And if there is tall buildings in the back ground with lights so much the better .

You're on your way but I'd recommend a couple things. Tripod of course. Turn off any image stabilizers. Set to f8, ISO 100. Shoot somewhat wide if you're using a zoom; if not, use your shortest lens. Turn off AutoFocus and focus manually to infinity and back off a smidge.
Use a remote trigger or cable release and shoot on bulb. When you hear the pop of the rocket being fired open the shutter and hold it open until the fireworks are over. (Try not to shoot through a window to avoid reflections.) Its also a good idea to cover your eyepiece to avoid any possible light pollution.
Don't let anyone kid you, you have to shoot "tons" of shots to get a few good ones. But who cares, nobody knows how many you took and your shots will be so much better than the cell phone shots your friends took they'll think you're a pro.
Attached is a shot from last July 4th using the above formula. (Please note, this is a single exposure not a composite).
Almost forgot; this was shot in RAW and processed in Lightroom.