The bulb in your projector may have been used for years already and could be as old as the projector itself.
The projector's 8 mm bulbs are no longer made. Resellers that stock replacement bulbs carry "new" old stock, or unused examples of a discontinued product that may have been stored in its original packaging for years. This means that when you purchase a "new" 8 mm projector bulb, it's really just an old bulb that has not been used yet.
An unlubricated fan or a damaged resistor can make your projector run at higher than optimum temperatures. An overheated bulb in a projector drawing too much current will burn out significantly faster than a bulb in a properly serviced projector with a well-lubricated cooling system.
Many novice projectionists turn off a projector completely and immediately after a film ends. Best practices for extending bulb life demand turning off the lamp first and leaving the projector itself running with the light outs so the internal fan can cool down the projector bulb. Give the bulb some time to cool down before you turn off the projector completely.