Hello! Congrats on getting a bunny!
Don’t fret. Your bun is probably just still adjusting to the new home.
When I adopted my bun, I made the environment as comfortable yet fun as possible. I set up blankets and grass mats on the floor. I also set up random toys and toilet-roll toys (stuffed with hay) on the floor as well. I also created hidey-houses out of cardboard boxes as well. I didn’t pressure my bun to leave his cage. Instead, I just hung out and went about my normal routine. Since bunnies are naturally curious creatures, my bun came out and explored his surroundings. Whenever he approached me, I simply fed him a piece of alfalfa hay (as a treat) and pet his head. He would munch happily on the hay and return to exploring and playing around. Needless to say, he quickly became comfortable with his fun environment. Now, he’s king of the domain.
I should also mention that I set up my bun’s cage in my bedroom, where I spend the majority of my time whenever I’m home. That helps, too, I think. I travel on the weekends, so my bun also travels with me — but that’s another story.
I recommend just giving it time. However, if your bun seems lethargic, isn’t eating or pooping normally, then you should consider taking her to a vet for a check-up. Otherwise, your bun just needs time to adjust, and you both need time to bond with each other. For me, I started off simple — I pet my bun for a few minutes every morning and evening. That way, he became very comfy with me.
Also, you can use different types of hay as treats. For example, if you’re feeding Timothy hay, then you can just Alfalfa hay as treats (or vice versa). I adopted mine at 8 weeks, and I couldn’t feed him treats either, so I used different hay types as treats instead.
It’s all a learning experience. Good luck! I hope your bun comes out to play soon!