Well it seems that his ex is trying to sneak her way back in. If my ex was stuck for a place to stay, of course he is welcome to stay at mine (we're still good friends, broke up about 1.5 years ago), but he would get the spare room or the sofa. ESPECIALLY if it's just for one night. I mean come on. I wouldn't mind if he slept on the bed and me on the sofa/floor but I would never think for a second that he would share a bed with me, and I know he'd be the same.
I get that you think your boyfriend is lovely for letting you move in when you were stuck and when you weren't even official, but the fact is, you're official now and there is absolutely NO NEED for him to share the bed with her. He clearly still has a soft spot for her. I know it's difficult to hear but it's true. Since there was no bust-up to their break-up, perhaps they still kind of feel like a couple?
You need to tell him how you feel, and that there is no need for her to stay in the same bed as him. Why do you have to leave for the time she is there? You live there too now, right? Why hasn't he told her that he's got a new girlfriend? He's clearly leading her of if he's not telling her that he has a new girlfriend and letting her sleep in bed with him. If he had any respect for you, it wouldn't've happened in the first place. I think you're being really naive if you're going to let him do it again AND let him go away with her. Did he ask you if you wanted to go?
He's being totally out of order, in my eyes. If my boyfriend did that to me, we would be having words.
...to become a pro gamer?