Just ask her to come over and hang out. you can do this toward the end of doing something else together or just as it's own thing. You don't even have to mention your room.
I remember this one girl I was seeing, we came back to my place after dinner and my roommates were home so I thought it'd be cool to hang out with them in the living room, she knows them a bit. I thought it might be strange to just drag her into my room; we usually hang out in my room, but it's when no one else is home. However, I went into my room to empty my pockets of car keys, phone, wallet, etc. When I turned around to go back she was already walking trhough the doorway. I hadn't even been gone 15 seconds, but I wasn't going to go back out now.
Just get her over to your place. Your room will be a natural place to hang out. Just relax and as long as you don't think it's weird to be hanging out in your room, then she won't think it's weird either. All your stuff is there and hence.. a lot of what there is for you to do.