What determines the amount of time a lightbulb will last?

Depends on way too many factors to predict.

Most lightbulbs are rated to last a certain number of hours under normal circumstances. Dividing the predicted service life of the bulb by the amount of time you use it should give you an approximation of how long the bulb will last.

Nominal 120 VAC commercial power can range from 114v to 126v. If the voltage in your mains is at the low end your bulbs should last longer than if it is closer to the maximum. Power regulation can have a lot to do with it; the same power surges that can kill electronics can cause light bulbs to burn out or reduce their service life. I noticed that after plugging a lamp into my computer surge protector instead of the unprotected wall socket that my bulbs seemed to last forever. Shock and vibration can shorten a bulb’s life. An incandescent bulb screwed into your garage door opener probably won’t last nearly as long as one screwed into a fixture in your ceiling. Also consider that there is variation in any mass production system and some factor light bulbs will work longer than others.