I set up their cage and leave the door open so they can come out into the room if they want. My first bun was a baby and definitely not ready to leave his cage. I left him along for a few days, but eventually I had to pick him up and bring him out of the cage. I think he didn't realize that he could jump out (the walls were pretty high) and once I showed him how he was in and out all the time.
My newest bun has lived in a home for 3 years, so when I put her in her cage she was already fairly relaxed and comfortable. I knew she was high energy, so I let her come out and explore in one room (didn't give her too much room too soon) because she was comfortable with it. If she didn't want to come out I wouldn't have forced her.
I've taken Otto to at least 4 different homes, two where he was left with strangers, and he's done fine. Hopping around, exploring, eating, etc. I don't think that all bunnies will automatically be scared and want to stay in their cage for a few days, so I let them tell me how comfortable they are.