Worst case of 19 drops: Drop bulb a every ten floors starting with floor ten, extending to floor 100. When bulb a breaks, start with bulb b. Drop bulb b start

Worst case of 19 drops: Drop bulb a every ten floors starting with floor ten, extending to floor 100. When bulb a breaks, start with bulb b. Drop bulb b starting from 9 floors below the floor that bulb b breaks, and extending to the floor directly below the one the b broke on. You can probably optimize this a bit by adjusting how many floors you jump with for bulb a, but 10 seems like an easy number.