Bullet Bill is a normal bullet that can be defeated by doing pretty much anything to it as long as you don't jump in front of it otherwise you will die or lose a power up.
These Bullets come from a cannon that fires them from the direction they are pointing at and where you are, so if your right in front of it and its aiming at you then it will fire but it also fires the opposite side to where its aiming at you as well so when you jump over it, it will fire from the other direction.
Another relative of it is the Banzai Bill which is much bigger then the Bullet Bill so you can expect it to have a bigger cannon then the Bullet Bill. Other relatives are Torpedo Teds, Bob-ombs, and Heat Seeking Bullet Bills and Golden Heat Seeking Bullet Bills.
Some Bullet Bills in some games (Super Mario Galaxy ect) will home in on you. These are Heat Seeking Bullet Bills.
In large groups or in particularly tight spots, they can give trouble to players.
In a game theory, a popular Youtube gaming speculation and statistics channel, it is shown that bullet bills should be very weak, due to their relatively low speed but high mass. However, larger bullet bills, such as a Banzai Bills or Golden Bullet Bills, are capable of dealing the real damage.