Welcome to BB! Also, good job convincing your parents to let you get your bunny spayed. She will be much happier and healthier than an unspayed bunny.
My bunny, Liebchen, isn’t big on being held. I have to get her with towels and scoop her up to do anything that requires holding her. After getting spayed, she was so tired she didn’t really mind. Chances are your bunny won’t put up as much of a fight as usual, but yes, you do need to check the incision. I would ask one of your parents to help you out. My Dad or my boyfriend always helps me anytime I need to pick up Liebchen.
Liebchen HATES car rides. She thumps the entire way. Unfortunately, the low-cost spay/neuter clinic was about 30-45 minutes away – she was not a happy bunny on the way there. She seemed kind of doped up on the way back and didn’t mind the ride. Some rabbits dislike car rides, and others don’t mind them – it seems like most actually don’t mind them. Even if your bunny does mind, he/she will be okay.
Since it was a low cost place, I followed their typical protocol. Dropped Liebchen off first thing in the morning, I think it was at 8 am, and I picked her up at pickup time which was 5 pm. I don’t think regular vets do this, though, so the time between drop off and pickup will be shorter most likely. Liebchen was tired at first, didn’t want any treats, but after about 6 hours she had some fresh thyme, after 12-14 hours she was eating pretty normally.