Why does a light bulb activate an infrared sensor? Is there a way I can filter this out?
Yes, a light bulb will put out some infrared light. 

Decoding remote control signals isn't that hard - there is a tutorial at instructables - http://www.instructables.com/id/The-Easiest-Way-to-Use-Any-IR-Remote-with-Ardiuno/?ALLSTEPS

This also means you can tell the difference between different buttons.

P.S. - when posting in this forum, it helps to include your code and your wiring.