One possibility is that your residual pressure valve in your master cylinder might have been leaking. When that happens, it allows the wheel cylinders to ingest air past the wheel cylinder cups. As for the master, yes, I believe that the flared end of both cups goes toward the outlet of the cylinder. Here's an exploded diagram:
http://chevy.oldcarmanualproject.com/gmc/5559mm/5559mm175.html
