Every entrance to the UC Santa Cruz campus is marked with signs telling you what to do if you meet a mountain lion. The answer is:
Look as big as you can, and try not to resemble a deer. So: Stand off the bike. Stand tall. Spread out your arms and jacket to look bigger. Speak to the cat in a loud, determined voice ("GO AWAY! LEAVE ME ALONE! GO HOME! GO CATCH A DEER OR SOMETHING!"). If you have something handy that you can throw, without having to bend down to pick that something up, then throwing something (keys, bike tool) at the cat can be helpful, but only if the cat has an escape route that doesn't entail running right past you. Do NOT try to outrace the cat (they're fast and like running prey). If you're in a staredown situation, keep your eyes on the cat and back off slowly. If worst comes to worst and the cat attacks, fight back (as opposed to with bear, where some say playing dead with vulnerable bits (belly, face, neck) covered can help).
The year I was there one mountain lion encounter was reported by student headed home at night across a footbridge right near my office. He came up against a big cat towards the end of the bridge. The cat did take a swat at him, but he followed the recommended procedures and the cat turned and ran away.