Your mum's being unreasonable BUT, she's your mum. Soon, you won't be under her control so much, but she'll still be your mum. Don't get cranky with her, try to talk her around, ride as she wishes where it matters and, like every other teenager since Adam had his first kid, do what you like when out of sight. JUST DON'T GET RUN OVER!
Hell, I'm 61 and would hate to have to live with mum and dad again but by the same token, I worry like heck about my own kids. Cripes, I even worry about the cats and they aren't even allowed to have bikes.
It's frustrating but live with it. In a couple of years, it won't be an issue.