Which Battery pack use for Arduino TimeLapse dolly
Assuming the motors are running the whole time you have 330mA for the motor. What the Arduino and driver will consume depends on a number of things but I'd hazard a guess of somewhere under 100mA so for a round number and a bit of a margin we'll say the whole lot is 500mA or 0.5A.

Driving everything from 12V is the easiest (but not most efficient) solution so for three hours of operation so you'll want a 12V 1.5Ah (3h x 0.5A) battery. That could be something like an SLA battery or maybe 10 x 1.2V AA rechargeable cells. 

You can also get 11.1V LiPo battery packs that are often used in model cars etc and that should be close enough to drive your motors well and will be smaller than the above two options. 

You'll need a charger for those options, there are a lot of choices so it really depends on whether you want to shell out for new charger or maybe use something like rechargable AA cells where you may already have a charger but using ten will be less convenient. For occasional use you could also use eight alkaline cells. You'll certainly need something larger than a 9V PP3 battery.