I mostly shoot revolvers in Bullseye, but if you are going to shoot semis it's pretty critical that you have at least three magazines that are extremely reliable for your chosen gun/ammo combination. There's nothing more vexing than being forced to refire a string, and it almost always lowers your score on that round and puts you in a bad mood for subsequent rounds.
Dry firing is helpful to develop a steady trigger pull. Read up as much as you can on Bullseye for proper stance and breathing techniques, doing everything the same every time, etc. This is a good site - http://www.bullseyepistol.com/
Good luck, Bullseye is a great competition that will make you a better shooter.