Definitely talk with your parents first, see if there’s any kind of compromise you can come to agreement on with them. If they are not willing to help you, see if you might have a friend who would be willing to house the bunny if you paid for all the bunny’s things?
If the uni lets you bring pets as sleepy said, I think that would also be a great alternative.
If worse comes to worse, I would talk with the current owner, go over the requirements/guidelines but also see if the new adopter will also be willing to talk with you before adopting so that you can be at peace knowing who the bunny is going to. That way you will also have a say so in approving or disapproving.
When I am rehoming a pet I rescued off the streets, I typically tell the new owner that if it doesn’t work out for whatever reason, to contact me & I will take it back. They’ve usually been pretty understanding of that, it was kind of them to contact you prior to rehoming it to let you know what’s going on. Maybe they wanted to give you the chance to take it back before they sell it to someone else?