Yeah, 70s Schwinn with an adaptor will take a 68mm BSC-threaded BB,. which basically means any BB marked 68x___mm. The question will be with filling in those blanks; chainline is pretty important, especially on a singlespeed or internally-geared hub, but also important on derailer set-ups. A lot of older 3piece cranks and square-taper BMX cranks need a really long spindle, often about 127mm. Newer stuff and you might want to be in the neighborhood of 110 to 118mm, but you don't wanna guess. You'll want to decide on what hub and crank you're using, figure out the rear chainline, and then do some measuring/thinking/research on how much spindle you'll need to keep that chain straight and parallel between the front and rear sprockets.
Some of these BBs are cheap, but the price adds up if you keep getting the wrong size and buying another to replace it. Also, running one that ain't right but "seems" to work fine is false economy; skewed chainline will wear chains and sprockets faster, and lead to the chain derailing. There's a zillion tricks to fine-tuning chainline once you get within a few mm of perfect, but if you're too far off, you're gonna need to buy new parts...
