How much voltage does a 15 watt bulb pull?

Flourescents other name is an arc-tube. There's an electrical arc(which is what makes the light by ionizing the gas) that occurs through the low pressure gas inside. It takes a lot of voltage to start the arc(to ionize the gas), and less voltage to keep it going once it's started and the electrodes heat up(becaue now the gas is ionized, hot, and a much better conductor). So a constant voltage is not the answer to properly running these types of lights. The transformers for these bulbs represent a high-impedance voltage source. So when the load is light, the voltage is high. And when the load is heavy, like when the gas is already ionized by the high voltage and current is flowing through it, the voltage drops severely so as not to send too much current through the gas. This is what you need to properly drive the light. This is why inductors or transformers are always used in the drive circuit. They can give high impedances without losing too much power.

A 15W bulb is on the small side. So I'm thinking it would take like 1-2KV to get it started.

Practically speaking, you would have to purchase a

transformer rated for that particular bulb (assuming

enough is left of the fixture to mount a new "ballast").

Fluorescent bulbs require close current regulation.

The voltage needed to drive the correct current depends

on diameter (T-6, T-8, T-12), length, and other factors.

Ballasts generally increase Voltages, and choke current.

You can't drive a fluorescent from a wall socket.

15 Watt Bulb

It requires 120V through a ballast to start up the light. The start up voltage as high as a few thousands volt peak generates from the ballast.

Your light has a built in step up transformer called a ballast you run it off of 120VAC. It uses 15 watts to run it.