Ohh!! This is such a great question for me to be answering!
First of all how old is your rabbit and are you planning on getting a kitten? Female or male?
My family got a cat when my sweet ol’ bun was about 6 years. We got a Devon Rex, which is very similar to the Cornish Rex. What we did the first couple of days was that the cat stayed in a different room the entire time. After a week of that, we let the bunny sniff the cat while the cat was in a carrier case. That way, the bunny feels secure and comfortable inviting this new creature into their home. After we did that a couple of times we let the cat explore a little of where the bunny was staying (Hallway, living room was the main areas where the bunny hung out). We kept a very close eye on both of them, just in case anything went wrong. Things went really well. Then as time went on we let them hang out more and more until they were friends. They would play together occasionally but funny thing is, my bunny was the dominant one. So her word was final. If she wanted to be left alone, the cat just went away.
Now, we had a huge outside pen connecting to our front door. What we would do during the summer was just to open the door and let the bunny come and go as she pleased. Now adding an inside cat to that made things difficult. Of course the cat wanted to go outside but with Devon and Cornish Rex they aren’t the best outside because of their fur, and also their sense of direction sucks. What we ended up doing was we set up a run line, like people do for dogs, between two trees and then we had a harness on the cat and the bunny could run free (it was fenced in, but the cat could jump it easy). That way, the bunny could leave out of the cats reach if anything went wrong and we weren’t watching.
Now one time, a neighbors cat jumped the fence and thought my bunny was going to be a fun snack. Poor cat didn’t know that my bun had cat experience AND a cat friend. For one, my bunny chased off that cat biting the tail, and two my cat helped! They were both very proud afterwards and got a very nice snack (while we looked them both over for any injuries)

As an added bonus I still have a picture remaining with them two together in our pen outside!

https://www.youtube.com/watch?v=DkNSykr1Eio

Well, when we got the cat it was just a tiny kitten, so she learned very fast when not to piss the bunny off and how she would be punished for it. And yes, the cat slept in our rooms (or where ever she fell asleep, it is a cat after all) And yeah, after a while we just let them both run the house. The bunny we would put away during night times because we didn’t want her to get to the tv wires while we were sleeping, but she had the entire hallway and her own cubby under the stairs.

@Roberta Omg.. that’s down right adorable!<3

Keeping a cat with a bunny, or any small animal, highly depends upon the disposition of the cat in question.
I have had cats that I would not trust in the same room, even restrained for fear for the bunny; but others like Zoey, I know are perfectly fine.

Zoey (cat) originally got to sniff our hands after handling Pete, then we move on to letting her see him from a distance in his cage and attached play area. They got to spend time in the same room with a gate in between them and highly supervised for some time, and whenever one of them got a treat the other did, too. I wasn’t overly concerned with Zoey from the start since we’ve had her for 9 years and every time she sees a creature smaller than her she tries to adopt it (kittens, hamsters, baby squirrels… take your pick); it was the same in this case–she just wanted to mommy him.
Some cats are natural born mousers though… so it would take more time and patience to train them that the bunny is family, not food. In some cases you may never be able to keep them together unattended. It really comes down to their personalities. I would highly recommend that you try to associate anything positive for the bunny being positive for the cat, too. Ours get treats and meals together, and if one is getting attention usually the other will try to butt-in.
Both have full-run of the house, day and night; but there are plenty of places that only Pete can fit behind/under, or only Zoey can get up onto.

Roberta that was cute.
Dadoo : I love the pic. Can’t say your kitty looks to happy about the harness though. lol. still cute.

Cottontail; Um.. That was her natrual happy face.. She wasn’t a pretty cat XD