Welcome! It makes me very happy to read what you're hoping to do. I'm pretty sure this site can help (lots of great advice here and plenty of experience). As far as resources - here and Ilfordphoto.com can both help. Ilford makes fantastic B&W film, paper, and chemicals (they aren't the only ones who do, but their stuff is very consistent). Their website has info areas with lots of basic info. Lots of info here, too, of course. Source for "stuff" - if you're in the US (not sure where Eastbay Area is), freestylephoto.biz is great. Once you compare what Ilford says you need to what you actually have, Freestyle can probably fill in the rest. Or the classifieds here.
As for whether it's the bulbs, that's tough to say without looking at them, but that's a pretty good first guess. And Freestyle carries bulbs. You mention Beseler, but which model? I have a 23CIII and a 45MX and the instruction books for both, I think.
If you're lucky, there might be a member here who can stop by and help you out. I know I would if you were close enough.