Welcome, Womble,
How long have you had Terry? If she’s still pretty new to your home, I wouldn’t worry.

Must bunnies view their houses as a safe place for the most part. They explore the outside territory in ever widening circles. And they are creatures of habit, too. She probably is checking out your home slowly, then going back to safety. As time passes she will venture farther and longer. Just watch to make sure she eats and poos regularly, and isn’t hunched up in her cage or grinding her teeth loudly, as that would indicate there’s a health problem.

It’s good that she lets you pick her up and is comfortable with you. You may actually be giving her too much freedom. Can you build a little enclosure outside her house so she can spend some safe time within a confined, but larger, space? A dog exercise pen is perfect for that. Also, you can attach NIC cubes to make an sort of fence. If you can close off the room she’s in you could just let her run in there (be sure to bunny proof it) and sit on the floor to keep her company. They learn quickly, and you’ll be searching for her all over the place in no time.

I bet she likes her house. What is the set-up like outside of the cage? Do you have boxes or tunnels or things for her to play/hide in? My buns don’t generally like a big, open empty room, they kind of make their way around the sides and they love hiding under tables or in boxes…

My bunnies really only run around and play in 5 minute segments. They will jump around and binky for about 5 minutes and then lay down for a nap. It sounds to me like she really likes her house and feels safe in there so thats where she goes when she is tired. Does she have any hidey boxes around the house to play in? For my bunnies I just take a cardboard box and flip it upside down and cut a little tunnel in it so they can run in and out of it. That might encourage her to play some more outside of her house. Also, the tunnel that Beka mentioned is a good idea. At Home Depot or another home improvement store you can buy these big cardboard tubes that are concrete forms and they are GREAT for bunny tunnels.

I agree, it’s probably her fav nap spot. Is there a ramp she can come and go on? Rabbits tend to just sleep the day away, even though it doesn’t look like it, with their eyes open. You might find her more active and willing at certain times of the day/evening.

I’ve had my bun for a month and he still won’t go more than 5ft from his cage + xpen area, so I wouldn’t worry about it. It’s a good sign that she really likes her cage! My bun spends the vast majority of his time in his cage or in his maze haven, with only short excursions out into the wider world. And when he does come out of the xpen area, he likes to stay along the walls or under the dining room table. Do you have nice hidey places near her cage? She might feel more comfortable coming out if she doesn’t have to be in the open too much.