Busted is a term thats been used throughout GTA games.
It appears on your screen when a cop/SWAT/FBI points his gun at you. This usually happens when you car gets stuck and a cop is able to run to your car door. Other occasions can be when you fall of a bike or are knocked to the ground, cops will take advantage of this and bust you.
On GTA3 you could avoid being busted by parking you car against a wall and looking away from it by pressing L2/R2 and this would lock the door.
As your wanted level increases and you have the SWAT/FBI/army after you youre more likely to be Wasted as they tend to shoot at you instead of trying to bust you.
THe outcome of being Busted is loosing all your weapons and $100 as a bribe to be let out. This is similar to what happens when youre wasted .