In general there are 2 challenges with bicycle mounts:
1. Not getting the bicycle in the camera field.
Vibrations are the biggest problem because they creates various forms of blur on the images.
Other people have reported that you shouldn't drive faster than about 15 km/h with a phone mounted on a normal bicycle on good pavement, because the vibrations creates "rolling shutter" blur. I gave up using a phone on a bike the first time I tried.
My experience is that action cams work great on a bike, even in rough terrain. As long as there is normal light. In bad light, like a forrest, take it a bit easy with speed and it is often okay.
Action cameras should be mounted as firmly as possible to the bike, to avoid amplifying vibrations. Unless you have some really good equipment, that means mounting it as close to the bicycle as possible.
I had a cheap plastic mount that allowed me to pan and tilt the camera, but the camera would vibrate so much that I got blurry pictures. Usually I use a flash light mount, that holds the camera close to the handle bar.
I have also tried the Manfrotto Magic arm with the Manfrotto Super Clamp. Because the arm will put the camera far away from the bike, it is not use able when riding. If walking it can usd.