I always had bikes as a kid, only raced once because there was no way my parents were going to miss going to the cottage on weekends. After the sacrifices they made all winter for my brother and I to play top level hockey giving up the summer was something that was not going to happen. I bought my kid a bike so him and I could trail ride at the cottage together. I signed him up for a Beginner clinic put on by the MMA so he could get riding tips and advice from a better rider than myself, he's been racing ever since. Obviously your parents can't be anti bike or you would not have the one you bought so you are one step ahead of some. Don't pester them but make sure they are aware how important this is to you and how hard you are willing to work to make it happen (keeping up your grades, chores at home, working part time to pay the costs of racing etc) and hopefully they will come around.
As far as rules regarding protective equipment there is nothing I'm aware of in the waiver you sign on practice days. If you are not 18 you will need a parent to sign the waiver for you. That being said I'm all about the best protective equipment you can afford so do yourself a favour and get a chest protector, neck donut, and knee guards at the very least.