We have Cheech in our bedroom and we let him out in there too. We found that just opening his cage door and letting him run out means he goes back into his cage at regular intervals and then after about half an hour to an hour when he goes back in we can just close the door and give him his daily treat as a reward. He doesn't like being picked up although he is very affectionate and loves being tickled so this works best for us.
Chinchilla proofing:
We have wooden boards that we block the bed with so he can't get underneath. They are just old shelves and it also hides all the stuff we keep under there from visitors so it makes out room look a lot tidier anyway.
When he is about to come out we stuff towels or pillows under the clothes cabinet to block it off (and down the side as well). He has learned to squeeze himself down the side of the mattress too so now we just put pillows or towels or a dressing gown down the sides of that too. It only takes a few minutes to set it up and then he has full run of the room. We turn off all electrical equipment he can get to like the PC and unplug the wires. Sometimes he will go up to chew them but as he is supervised the whole time we can tell when he's going to do it and give him a sharp no. He learns very quickly as most chins do, but because they are unplugged if he ever did chew then it wouldn't harm him, but we would have to buy a new wire.
Just make sure anything like TV remotes are put away safely, and not just on top of a cabinet because your chinchilla after a week or two of getting used to the room
will find a way up there and s/he
will nibble them! We just had to buy a new control pad for the Xbox 360 because I accidentally left it out on the bed and Cheech took a chunk out of the thumb stick with one bite, and they're not cheap. Bless him.
At first it will seem like a lot of work and take ages to set up, but if you have the same routine ever day then soon it becomes second nature. My boyfriend can even watch TV while Cheech is out because the wires are all behind the cabinet safely out of Cheech's reach and I can watch the little monster in comfort.