If the bulb was infrared then we wouldn't see it.I'm pretty sure that coloring the bulb red has anything to do with making it infrared.
A normal bulb white or yellow emits visible light and UV rays. Wrapping or coloring it doesn't change the color spectrum from Visible Light to Infrared on the spectrum scale I believe it has to do with the filament inside.
I've tried to do more research on this from howstuffworks.com and google but can't find anything. I know from that site that "Incandescent light bulbs give off most of their energy in the form of heat-carrying infrared light photons -- only about 10 percent of the light produced is in the visible spectrum"
I assume that is why we can see the light from the normal IR bulb we purchase for our heat sources. Then when you think about your TV remote and the IR signal/light it emits we can not see at all.
Not quite sure why I have written all this but I was curious and still left unsure. Just go out and buy a bulb which is labeled "Infrared"
Quote taken from http://home.howstuffworks.com/light-bulb2.htm 7th paragraph
Images taken from http://electronics.howstuffworks.com/nightvision1.htm under 1st paragraph