First off, have you done a lot of research about buns? They're not just a cute, fun pet. They take a lot of time and consideration to care for, and I did a lot of reading about them online before I made the decision to get Sara. They live for a long time (8-10 years) so if you're going to college anytime soon your parents will probably have to take care of her. Another thing to consider is whether your family can afford her - I spend ~$30 a month between hay, pellet food, and bedding, and that doesn't include toys and snacks. Setup costs are expensive too - a cage will run $80, and adopting was $70. Fortunately the Humane Society at Petco had a deal where if I got the bun, I got the cage for free. Yay!
Another thing to keep in mind is that buns need to be let out of their cages for at least a couple of hours a day and need human interaction every day. You have to be careful that they don't chew on anything bad like cords. Also, and this was the biggest thing I didn't know, is that they can be LOUD. Sara will rattle the bars of her cage and make a lot of noise at 6-6:30 in the morning wanting breakfast and attention. I stay up late, but even if I put her to bed at 10 or so she will rattle the bars for five minutes or so before settling down. I don't get to sleep in anymore!
If you do your research and make it clear to your Mom that you are willing to take responsibility for these things, and can maybe help more with chores around the house to offset the cost of the bun, that would probably help. Also, tell her about the research you've done and why you think a bunny would be a good pet, NOT just because they're cute. They're fun, sensitive animals but don't act like dogs or cats. A lot of buns don't like to be picked up, and some aren't big cuddlers. Mine loves to be scratched but won't come to me for it and isn't a lap bun, nor does she like being picked up. She also isn't very interested in playing with toys. Would that be ok with you? Buns have weak spines and if you drop them they can be severely injured.
Good luck, and I hope with more information and suggestions for compromises you and your Mom can work something out! They are great, loveable pets if you're willing to invest the time to get to know them