You're parents must have their reasons for not allowing you to have a bunny at this time. I'm not trying to side with your parents but maybe they feel the responsibility is a little too much for you at the moment? Maybe you have alot of other activities going on and they might come into conflict with the bunny's care.
How about volunteering at a SPCA or Humane Society, or a rescue group in your area and getting to know the care and time it takes with each animal as an individual? There are plenty of groups that would LOVE to have your help! You could snuggle and care for a bunny or kitten or cat....or you could walk a dog and get sluuuurpy dog kisses! That sounds like an excellent beginning for an animal lover such as yourself! Just volunteering your time and love to an animal (imprinting love) would do wonders for your self esteem and for the animals you are helping!
Perhaps after you have shown your parents through your diligence of caring for critters that are NOT yours, they might reconsider. But it won't take just a week or month of your time,but many, many hours of selfless involvement. You might even find your place in life through volunteering!
I have an enormous stockpile of rescue groups that ALWAYS need someone to help. If you could tell me whereabouts you are I could post a list of great rescue people that would be in contact with you. But remember that besides all the sluuuurpy kisses and cuddles comes the work of feeding,cleaning the poop and all the other "downsides" of owning a pet.
Let me know if you'd like some help in contacting someone!