Well, if I remember correctly, the BB's on modern bikes are all pretty similar, except some have funky threading (Italian, French, Canadian). The only difference would be the spindle length, which really you only need to worry about if you have a super off chainline. Unless you get a wierd old school Gitane or something like that, you should be able to transfer all the components between the two bikes. If you say it is a smaller bike, I would recommend getting a larger frame ASAP. When I finally got a frame that fit me, I was shocked how much easier it was for me to sustain a longer ride. Now I ride bikes that are borderline too big for me, but still I love em and could not imagine riding anything smaller.

Phil

P.S. I am sure if you needed help, there is quite a contingent of Chicago fixed gear riders on this forum, or you could come out to Minneapolis...