A while back when I was on a bike ride, I encountered a Bobcat along a canal.
The one I saw must have been well-fed because he was much bigger than this one.

Bobcat
Nothing happened; I saw the Bobcat, stopped riding, and waiting for him to go away. After a few minutes, he went into some bushes and disappeared from view. However, I kept an eye out for him as I passed the area where he was walking. My ride continued on and I had no further encounters.
According to the Arizona Game and Fish Department, when it comes to a Bobcat encounter the best course of action is to not panic:
If you see a bobcat…there is no need to panic. Bobcats rarely attack people. However, if a bobcat does attack a human, it generally will have symptoms of rabies. Bobcats may be attracted to a yard that has abundant wildlife, domestic birds, small pets, water, and shade or other shelter.
The most important thing to remember with most wildlife encounters is that wild animals want to be left alone. If you don’t attack or threaten a bobcat, snake, wolf, skunk, or other creature…it won’t bother you. With that said, be on alert and aware of your surroundings wherever you are. Many wild animals can be found on the periphery of metropolitan areas so chances are you will encounter a wild animal if you live on the outskirts of town. Be smart when you encounter them and you won’t have anything to worry about.
Bonus: Here is a short video from a local news channel bobcats visiting a backyard close to where I live.