I guess running your dog with your bike needs to be in a controlled environment. I’ve skidded off my bike twice this year bruising my knees and elbows due to the high pavement and loose gravel. I’m lucky there were no cars behind me. I think you’re asking for an accident to happen. Where do you live that you can do this? Too many people, dogs, motorcycles, kids, trucks, etc. Bike riding alone is dangerous enough here. Maybe on a bike path in a rural setting. I think the solution is to not do it!