This is a great question even though it’s sad to think about.
If at all possible it’s best to let the bonded mate spend some time with the bunny that has passed. It is very hard to watch, but it helps the bunny that’s left behind to understand. I don’t know exactly how animals perceive death but they do seem to understand that their buddy is gone. This can be beneficial for them to move on. Some bunnies, who have not spent time with the body, will just wait for their buddy to return or spend time looking in the usual places. Very heartbreaking.
The body should be left with the bonded mate for a little bit – As far as how long the body should be with the the bonded mate depends. Some bunnies get it within a few minutes, while others may need a few hours. My vet said that once they realize it, they usually move away from the body and won’t go near it. Jack took only about 15 minutes to figure it out. This next description is rather sad so if you (or anyone)doesn’t want to know how he came to realize it, then just start reading again on the next paragraph down below. —– A few minutes after Rucy died and I said my goodbyes (she died in my arms), I placed her near Jack. Jack, at first thought she was just sleeping. Jack, being Jack, at first tried to mount her, but then just as he was about to mount - before he made any mounting movements, he stopped abruptly, backed up a bit, and started sniffing her with definite confused interest. He then tried to lick her eyes, which didn’t close. He seemed confused at first, and then he froze for a few seconds – it was like he figured something out and just left her. Her body was left there for an hour and half , but he wouldn’t go near her. (just as my vet said would happen)
That didn’t mean that he still didn’t go through a grieving process. And he did still do a couple of looks up to an area where normally she would lie, but he started grieving right away and wouldn’t eat much. So we spent much more time with him. I worked from home, so I brought my work into his area, and just sat near him. I would then pet him more during meal times, and that made him eat more. He wouldn’t eat much by himself. It took a couple of weeks for him to just eat without company. I also gave him a bunny toy that kept our other bunny Bailey company for years befoe she passed away. He then hung out with the toy bunny.
Here’s are some good articles about this very subject from the House Rabbit Society
http://www.rabbit.org/journal/2-1/loss-support.html
http://www.rabbit.org/journal/4-7/bereavedbunny.html
http://www.rabbit.org/journal/4-7/love-goes-on.html