A large battery can power a tiny device. It's not a problem (but there is another problem). Battery do not just output current blindly. They output what the load draws from them (up to a maximum current draw determined by the battery).
You say your battery is 7A. Do you mean 7 amp-hours? A battery that outputs 7A is capable of outputting a maximum current of 7A, while a 7 amp-hour battery (in theory) can provide 7A of current for on hour before becoming empty. If you draw current from the battery half as much (or twice as much) the battery lasts twice as long (or half as long). But in reality, it's not nearly as good as this due to internal resistances in the battery and other things like that. I am betting you mean 7 amp-hours[Ah] rather than 7A. It is a measure of energy capacity.
The real problem is that your bullet camera is a sensitive electronic circuit, and your motor cycle battery is probably powering other things...larger things that make lots of noise and voltage spikes that could destroy your camera. Also, the battery voltage fluctuates which your camera probably doesn't like. Your camera might have built-in voltage regulators but they are probably not rugged enough to handle the spikes from the other equipment your battery is powering. Then there is how your camera runs on 12V and the battery is 12V. Simple voltage regulators can only convert a higher voltage to a lower one (they have losses), meaning that a simple voltage regulator might not work since your battery and camera voltage are the same.
You are going to need to protect the camera from the spikes (this for sure) and regulate the voltage (this depends on whether it's your camera that needs 12V or whether it's the voltage regulator in your camera that needs 12V...Let's hope it's the second one since the purpose of a voltage regulator requires that it be able to handle imperfect input voltages.)
Do quads have some kind of power plug (like a cigarette lighter or something?) That'd make your life a lot easier.