I’d honestly try to keep the bun inside where it is or rabbit-proof your room and let them live in there. Outdoors will be tricky in the winter months with keeping your bun warm, or in the summer months with keeping your bun cool enough. I would definitely not go with anything you see breeders do– I don’t think they’re bad people or bad bunny owners, but I know a good breeder from a bad breeder, and most of the not-so-great ones house their buns in outside hutches with wire flooring. Generally speaking, the best breeders keep their buns indoors. Just because someone breeds buns doesn’t mean they know how to take care of a bun.
Plus, if your bun is outdoors, it’s not as likely you’ll go visit the bun for the hours you should every day, especially when it’s snowing and whatnot.
If you absolutely have to move the bun outside, a large shed is a good idea, but make sure you still get them outside-of-she’s time for a few hours every day, and in the summer put a fan in there, and make sure the shed has plenty of insulation for the winter.
Hope this helps