Originally Posted by legalize_it
to scare off a mountain lion you need to make it think that he/she is the prey and you are the predator. Bsktball55 has the right idea with using your bike to make yourself seem larger. make a lot of noise and act like you want to eat the lion. if the lion thinks you might eat him/her, then you'll be safe. or you can buy some mountain lion repellent.
You don't need to be a "predator". You just shouldn't act like prey.
Unlike the previous posters suggestion, I don't think keeping a bike in between you and the lion will help. They're ambush predators. You'll never see them until it's too late. If they allow you to see them, they're not hunting.
I heard an interesting story about rangers in India. They were getting picked off by tigers. Well somebody figured out that tigers never attack when they see eyes since they are ambush predators. So they tried wearing a mask on the back of their heads. The tigers stayed away. You might try affixing some silly mask to the back of your helmet to maintain "eye contact".
My other suggestion would be biking with a decent sized dog. The dog wouldn't win an all out fight with a lion. But the presence of another large predator is enough to keep a predator from attacking in the first place. Predators only choose prey that won't injure them.