Regarding the crankset: is there a model number and manufacturer embossed on the back of the drive side crank arm? If so, that might allow you to determine the BB spindle length and taper (ISO or JIS) needed for your replacement BB.
Regarding the old BB: did your LBS remove the remaining BB parts from the frame and return them to you with the crank arms? It's a longshot, but if it was an old-style cup and cone BB there's a chance that the cups are still serviceable. If so, all you'd need is new ball bearings and a spindle of correct length.
Square taper spindles are getting hard to find, though. Might be easier to find a cartridge BB of the correct spindle length instead.