With a fanny pack/chest rig, you are almost always going to have some bounce. I have spent a fair amount of money experimenting with various brands etc. Some were ok for walking but not running.
Also, most fanny packs don't come with a a built in holster or anything that protects the trigger, so you need a holster, as well as a fanny pack. Most of the ones that I've seen advertised for runners are not even remotely close. The one above with the shoulder strap, ain't gonna work for a serious runner doing serious miles. I don't even have to pray about that one. It sits up way too high the chest and that shoulder strap would rub you raw.
The VNSH holster keeps the guy tight to the body and covers the trigger. It is lined with yoga pant material and it which helps wick away the sweat. I have taken my gun off after a 5mile run in the Texas heat, the gun was completely dry.
Its also one of the better concealment systems I've seen. With a Glock 43, there is no way you could tell that I was carrying.
https://vnsh.com/products/vnsh-holster