Bicycles never needed insurance before. Can you find one at a local goodwill or other 2nd hand store. If you have been doing some dog walking you should have some money saved up?

Parents who are overprotective or controlling like this are hard to live with that is why many run away thinking a homeless shelter is better than the control. You will find a way when you are 18.

You are home schooled so you don't have the option of school driver training class like other kids have.

Why did your parents take you out of school? We're you being bullied? Do you have a mental condition that limits your abilities that your parents feel causes the need for them to protect you from the world?

I understand how it feels to feel trapped. At 16 I would not suggest walking there if your parents don't want you to go. They could call the police & report you missing which would just mess up the whole situation you are trying to figure out how to do as you are under age & your parents are still responsible for you.