My beater bike has simmilar issues and I suppose that since its a beater I haven't sorted it out yet but I too thought is was the BB but when I changed cranks to get shorter arms I also fitted a far supperior BB but it didn't change a thing. Its a clicking noise on my bike too and the funny thing with my bike is that it only happens on certain cogs. On the smallest cog and the 2 largest cogs its fine but when I'm on the middle ones it clicks!
Anyway I suspect that its to do with the rear derailer and the angle that the chains running. Its a cheap and nasty derailer so its probably so far out of whack that its not a supprise that its making a noise. I guess I'll sort it out one day.
Regards, Anthony