The answer depends a bit on what exactly the Question is/when the Bsod occurs:
(Large parts of guesstimation on my part involved)
I just noticed you meant BSoD, not CTD, so disregard the other stuff. BSoDs are usually (afaik) caused by faulty or missing scripts, ship(file)s or (Bridge-) animations. You should still be able to get a console printout, to help ascertain what exactly caused it.
-Also, does this happen when a specific ship or bridge is used?
If you mean "how many ships can BC handle at once"/ or the BSOD occurs after loading a QB with a large number of enemy/friendly ships (or ships with large textures):
I don't know, but not that many. It depends a bit on your hardware, but there is also a memory leak in BC's engine involved.
(As fas as I remember there was some sort of custom patch for that once, but I can't find it anymore)
Personally, I can run only about 10 Ships or so simultanious, or it gets really bad and CTDs after a time.
But someone stated to have run up to 40 ships at once, in the past.
If you mean "how many ships can BC(foundation) handle in total"/ It crashes upon first entering QB:
That number should be pretty much limitless (or as much as python allows it to). In any case this would crash on main menu loading, not QB entering.