Sounds like a regulator problem. With the scooter running and reved up you should be seeing less than about 14.5v across the battery terminals. If it's more than that bulbs will blow out quickly. The headlight and tailight bulbs will blow first because they are on all the time. If the voltage gets up to 16-17 volts, you might only get 1% or the expected bulb life.
If you're seeing more than about 14.5v across the battery terminals with the engine running and reved up, then the regulator is faulty. It can't really be repaired, you'll need to replace it. If there's too much voltage, it will also eventually damage your battery by overcharging it.
I don't think it's related to fuses at all. I don't know the bulb specifications for the Bandit 150z, but any nominal "12v" automobile, motorcycle or scooter bulb of the appropriate wattage and the right base should work fine. All auto bulbs are designed to work with 12-14v supply.
If it's not covered under warranty, a new regulator (if that is the problem) isn't expensive. $25 or less. The problem will be in figuring out just which one your scooter uses. Take a look at http://www.partsforscooters.com/All-Parts?search=regulator
for some examples.