When I wired my doorbell transformer to a light in my basement I followed the instructions and wired the white wire to the neutral wire the black wire to the black wire of the power source and the ground wire to the ground in the light. However, the light that the transformer is wired to stays on very dimly when the switch to the light goes off. It appears some power is getting to the light. When I disconnect the white wire of the doorbell to the neutral wires in the box the lights will go completely off. I'm not sure else how to wire the transformer?

First of all... does the doorbell work whether the light is on or off?
Are you sure you didn't wire it to a switch leg? It's possible that you wired the transformer across a switch leg.