Rubbing impurity on the ground

I ride scooters and bikes to school. I rolled over non-halal foods/sandwich packages with leftover foods several times when riding on the streets. I live in the U.S. and the sandwiches are subway wraps with wet food oil and sauce and certainly not halal. Hence, the bike tire becomes impure. When I ride it in rainy days, the water splashes from the tire onto my shoes and pants. Since the bike tire is impure the water splash is impure. I have to go back home and wash them every time I pray and it severely impacts my life. However, I heard that walking or rubbing impurity against the ground makes the impure shoe pure. Does this ruling apply to a bike/scooter tires? If so then the bike tire can be regarded as pure as it rubs against the ground so many times?