I’d try to make him as a comfortable as possible and try to acclimate him to some things:

1) Get him familiar with his pet carrier: I left Wick’s carrier open on the ground for a week before his first vet visit. He got to get used to it and sniff around it. A lot of people have success in their rabbits feeling comfortable in their carriers by rubbing a towel/cloth on the rabbit (or any other method of getting the rabbit’s scent on the fabric), then lining the bottom of the carrier with it. Pet your rabbit while he’s in the carrier as well.

2) Baby step-touches: Your vet will want to feel your rabbit, listen to its chest and heart, and other things. This requires a lot of touching and maneuvering of your rabbits underbelly. Maybe have small periods where you simply cradle your rabbits stomach (don’t pick him up, but just a cradle), and then calmly take your hands away. With rabbits that are not inclined towards being picked up/handled (which is many), it’s important to stop interaction on their terms, not yours. If you find a small step in-between no interaction and your rabbit’s limit, keep at that every so often until your rabbit seems ready to go a bit further. A good baby step (when your rabbit is ready) is literally picking him up half-an-inch off the ground, then placing him back, and petting him. Then you can increase the intensity by picking him up, moving him 3 inches, then placing him down. When I say pick up, I don’t mean dedicate into an arm-fold pick up; just a pick up with your hands around him. Some rabbits feel more comfortable when their bottoms are stable, so you can do one hand on the side/underbelly, then the other scoops from behind, under the butt!

3) Talking to your rabbit: If you talk to your rabbit, don’t be afraid to do that during your vet visit. I talk to Wick during my vet visits and my vet joins in, haha. It’s all a part of making the environment less scary and novel.

4) Treats: Have treats handy for the visit, because at the end of the day, the visit needs to be associated with neutral or good consequences, not bad ones (like being poked and prodded).

Also reward your bunny everytime he goes inside his carrier, use something healthy like lettuce or herbs if he decides to go in a lot

Personally not having my bun familiar to his carrier to his carrier works for me because it is “new(ive used it couple times” and he is very adventurous so he goes right inside