Characters with Marksmanship above a certain low minimum - like, 2 or 3 or so - should be able to control the size of bursts they make even with a weapon which is on full auto. At low levels they should be able to choose 5, 10 or 20; at medium levels add 3, and at high levels (Marksmanship 8+ or so,) the player should be able to enter a number of rounds they intend to fire between 1 and 20.
This would also make the trigger happy drawback more meaningful, as players with that flaw would still have an incentive to use firearms that go up to full auto, and thus risk ripping off a long burst, rather than just deciding that the flaw is free points by only ever using a semiauto for normal use and pulling out something with a full auto only at the times when they intended to do so anyway.
Instead of prompting the player before each burst, I would say that how it would work is that firearms with full-auto mode should have:
“Full Auto - Rock and Roll” that fires as many as possible. This would just be “Full Auto” if the player’s Gun skill is insufficient to control their bursts.;
“Full Auto - Long Burst” for 10;
“Full Auto - Short Burst” for 5;
“Full Auto - Three-Round Burst” for 3, all of which are replaced with;
“Full Auto - Custom Burst” when the player’s marksmanship hits 8. When the player selects this fire mode, they can enter a number, and the fire mode then displays “Full Auto - X Round Burst” where X is the number of rounds the player entered. Until the player attempts to switch off that fire mode again, that’s how many they will fire. If the player is using a weapon that only has the FA mode and switches fire modes, they enter a new number - such as if that nasty Shock Brute shows up at close range, you’re probably gonna want to enter ‘20’ and rock and roll.
This might have an additional advantage over switching firing modes in that switching the selector might take a (small) amount of time, whereas this is a declaration of the player’s intent and takes no time whatever. But that would require, I think, implementing selector switch use taking time.
As an alternative implementation to the above, you could have “Custom Burst” available at all levels, or even make it the only autofire option, and the player’s marksmanship determines how well they conform to their intentions - a character with low Marksmanship might fire too many, or too few, rounds.