An infinite number. Quantum mechanics tells us that there could be an infinite number of identical light bulbs in alternate realities, so if we want the bulb changed in all the possible realities then we will require an infinite number of scientists to change all the bulbs. The only hope is that one scientist per reality will be enough for each bulb.
Alternatively, quantum mechanics also tells us that if we wait long enough then the bulb will eventually change itself. This is because even though the probability of the bulb changing itself is extremely low it is now completely zero. So if we wait an infinite amount of time then the extremely low chance will eventually come to pass. However the time required to wait for this is almost incalculable. There is probably a greater chance of you spontaneously growing a second head or something?