Congratulations on your new bunny!
And congratulations to your new bunny for her new owner!
You’ve come to the right place for your question, there are many experienced veteran posters here who will provide you with precise and proper answers.
Unfortunately I am not one of those experienced folks, but since I’m just about rounding out a month of being a bunny owner for the first time, perhaps my unqualified thoughts will be helpful to you nonetheless.
1. I think the first thing you want to do is find out whether your rabbit has been spayed. The same rabbit depending on whether it’s been altered or not will be a completely different animal.
Since you have a female, it is highly recommended that you have your bunny spayed. The cancer rate with regard to female reproductive systems in rabbits is a crazy high number. Spaying her will eradicate the chance of that particular problem and will increase her longevity. It’ll also calm and relax her hormonal inclinations.
If she’s already been altered, great!
2. As to whether you should keep her original cage as is.
I personally brought my bunny home in a box full of hay, bedding, water, and I’m sure a whole ton of new scents. I didn’t have a choice though, the seller didn’t provide me with anything (not even an accurate age, even though he was born right in her rabbitry…)
I will speculate though, that at some point, it’s worth cleaning the cage. Both for her health and the general cleanliness of the environment.
Having her getting used to new scents and smells might make her uncomfortable, but then again, it might not. I think it really depends on the rabbit. But obviously, at some point, she’s going to have to associate her new home with the new smells.
3. As to how to interact with her.
My bunny was intensely scared of me. In fact, he was the most scared little bunny at the rabbitry. I did what I wasn’t supposed to and skipped the friendlier, braver bunnies and picked him out because I felt sympathetic toward how afraid he was.
I’d like to think we’ve bonded quite well. He’s no longer scared and let’s me hold and touch him all I want without any resistance. But before we get into this, there’s something you need to do and/or understand.
4. Make an educated and realistic assessment of your rabbit’s personality.
This is extremely important, and might be hard to do right now. Keep in mind your bunny is a prey animal and will be naturally defensive and mistrusting. If rabbits weren’t as cautious as they are, they’d have gone extinct many years ago. Some rabbits are shy, others are really friendly.
For the time being, your rabbit will be a bit scared, understandably. My bunny, for the first day or two, avoided me at all costs, and stayed inside his makeshift hut. If you do get a hut, I think one with open sides is best. If your rabbit can hide from you all day and night without having to see you, or you seeing it, then I think it could delay the bonding.
Make sure she can see you. Eventually she will realize that although you are a scary predator, that you aren’t interested in eating her.
Some rabbits like being held. Others don’t. Just because your rabbit doesn’t like being held, it doesn’t mean that she doesn’t like you!
5. Back to how to interact with her.
I would situate her cage with all her furnishings including unlimited hay and clean water, but don’t put the yummy treats in her cage. Animals learn through association. She will probably associate you with a predator at first. That is her natural instinct, and she is rather correct, humans are scary predators.
I even withheld the small amount of pellets I give to my bunny. No, don’t starve your rabbit, if she isn’t eating out of your hand, then make sure she has access to it where she can eat it alone. But eventually she will eat out of your hand and she will associate your hand, and more importantly, YOU, with treats and yummy stuff. That is how you might be able to break the ice, get her to come out of her shell.
Once she does, you may be able to make a more accurate assessment of her personality type. Once she isn’t afraid of you, she may even become curious of you.
At some point, rabbit proof an area where her cage is. Leave the door to her cage open. Put some treats near you (make sure she knows you have them, keep them in your fist and let her sniff it.) In the area, sit down and just start doing homework or do whatever you do on your computer. When she’s ready, she may approach you. A prey animal approaching a predator out of curiosity is a huge step, but it has to be on her terms.
Soon enough she may be crawling all over you! Mine climbs up on my shoulders. I don’t appreciate the bunny butt in my face, but I do appreciate the attention.
If she can approach you without fear, then try giving her pets. Rabbits like being stroked. Rabbits like to groom each other, and so, it’s possible when you pet your rabbit she thinks she’s being groomed and she will appreciate it.
6. Final words.
Just keep in mind there’s no definitive time-frame for all of these things. Depending on her past owners, she may be very distrusting of you. You just have to be patient!
I would also like to take the time to reiterate that my opinion is very much unqualified by any experience. I am a new bunny owner, much like you, and just sharing my experience. If my experience was going poorly, I wouldn’t feel inclined to share my thoughts, but since it seems like my bunny is having a great time, I feel like I am not giving you bad information.
Good luck! And congratulations again!