Trying to decide how large of a battery I will need to power light bulb.
A single battery? Not very long. You can look up battery datasheets. 3W at 1.5V is 2A. 

Even with an AA battery, a 2A discharge current is off the chart. Maybe constant power you could get a few minutes. AAA would be worse.  



Two fresh top-quality alkaline cells might be able to buy you 1/2 hour operating if you allowed the voltage to drop to 1V (that's constant current discharge, so much of the time you'd actually be getting between 3W and 2W. Constant power or AAA would be worse.