You are blowing this out of proportion.
1st of all cougars are very timid creatures. It will be rare that you will even see them. let alone be attacked by them.
2nd Humans are not their natural food source. So for a cougar to consider attacking you, They would need to be very hungry and just not able to find their normal food.
3rd Cougars are members of the cat family and act much like your typical house hold cat. They are curious and will chase something for the game even if they don't intend on killing/eating. Hence Don't run when confronted by a cat. As mentioned make yourself as large as possible. Noise helps. Be loud, yell, bang large sticks against trees, discharge firearms.
A cat may sneek up behind you to see just what you are, But once you make it feel uncomfortable they will usually flee and continue the patrol of their territory. In some areas where cougars are not hunted, they have become a little more accustomed to people. These cats might be willing to get closer and even challenge a human since they have no fear. This is usually triggered more by some body fleeing them, either because the person turns and runs away or they don't know the cat is there and they move past jogging or on a bike where they appear to be fleeing.
Cougars will kill and eat small dogs. I've had several ladies come around camp areas calling their little fluffy lap dog, claiming it went out to go potty and never returned. Cougar will snatch those small dogs up just like a rabbit. Most 150+ pound cougars can easily kill a 60lbs hound dog, But they run from hounds. I don't know if it's the fear of the pack or just a million years of genetic instinct telling them to fear canines that causes them to run. But they do.
As far as the woman that outran the cougar back to her car. Hog wash. If that cougar wanted to catch her. there is no human alive that can out run cougar. If that cougar has wanted to catch her, It would have been on her in seconds.
Go out and enjoy your normal rides. If it makes you feel better carry some Pepper spray. It works on the eye and nose of cougars as wells as bears. It will also make your eyes tear up and cry if the wind blows it back in your face. A gun or something else to make loud noises will also work well. Don't go out smelling like food. If you just killed a deer and butchered it on the mountain, clean up and get your cloths changed. Don't wear bloody cloths if you are concerned about predators being in the area.
I've spent a LOT of years in the back country of Utah, Idaho and Wyoming and have only seen a couple cougars that we did not find with hounds. They are extremely rare to spot. Consider yourself lucky if you get the chance.