Lots of ways to handle this depending on the level of granularity you want to go. Do you really want to track bullets? Do you want a more abstract way to track out of ammo?  Are there barrier to players having rapid firing weapons (cost, training, legality)?

Probably the simplest way is to represent the higher rate of fire simple as more damage against a single target. A lot of simpler games are OK with the one attack, one target sort of framework. You also simulate in Fudge spraying bullets across multiple targets by just counting the flat damage of the weapon and ignoring the level of success in those instances. That gives kind of makes sense in a more targets, less accuracy sort of way and in game terms balances the area affect vs single target.

Or you take it further, have recoill penalties, track ever shot in a burst... it all depends.

Lifting an idea from the TinyD6 games, you could ask for a situation roll at the end of each fight scene.  A Terrible Desi!the could mean that the PC is out of ammo, while a Poor roll could mean that the PC will be out after the next fight.

Linking ammunition to rolls during a fight might be another option, with low rolls representing a character needing to reload rather than missing.