Clarke I replaced a couple fluorescence lights with new ballast in the front of the coach with a more efficient fixture and bulb T8. There is an awful lot to know about florescent lighting. Not all fixtures can recieve just any bulb as the following web site will address.
http://www.servicelighting.com/libra...e_lighting.cfm
I also replaced a bulb such as the one you are having an issue with over my sink area with a LED light strip which works very nice, but I have to admit that LED's have a shorter lighting distance and don't think it would be enough for the bathroom area. For that i believe that richard gave you a good site for replacement ballast. It would be beneficial for folks to get a good understanding of florescence lighting because they are the reason for many fires when not used and cared for properly.
Brad