What Bottom Bracket for a 2007 Rush Hour frame? The stock rush hour bottom bracket is a FSA BB-7420.  Would a Shimano BB-UN54 that is 68 X 107mm work in that frame?
The frame is almost certainly a 68mm English-threaded shell.  Beyond that, the cranks you're using and the desired chainline determine the bottom bracket spindle length.

If the rest of the bike is stock, BikePedia claims that the crankset is a TruVativ Touro Track. The Truvativ Crankset docs specify a 108mm bottom bracket with that crankset giving you a 43.5mm chainline. Reducing that by a half millimeter or so by switching to a 107mm bottom bracket should be just fine.