Yikes! A double triple ditto regarding the replies so far. A rabbit should not be fasted! A rabbits digestive tract is always on the move and unlike dogs and cats they cannot vomit, which is many times the reason vets have cats and dogs fast. It can be hard enough to get a bunny to get his appetite and get his digestive tract moving again and to fast can make it doubly difficult which can create some serious problems with recovery.
Also, sometimes a vet will know not to fast, but the front desk people may not, so if this information did not come directly from the vet, then you should talk to the vet. If the vet said this, then I would really rethink using him/her.
Here are some previous discussions too about spaying/neutering
https://binkybunny.com/Default.aspx?tabid=54&view=topic&postid=13556&forumid=6&tpage=2#13954
First-hand advice & assurance: https://binkybunny.com/Default.aspx?tabid=54&forumid=2&tpage=1&view=topic&postid=17164#20010