You could repot your rose at any time when it wasn't in bloom (lots of stress on the plant if it's moved at that time). I'd go at least two sizes up when repotting--if it is in a gallon container, try for a three gallon container. That way there will be plenty of room for root development and you won't have to repot again for a while. I'm speaking from my experience of growing cuttings, which go into the ground after the first year, so you may get better advice on container roses from someone else here.
I've had limited luck with full sized rose as bonsai. I'm bumping this back up to the top to see what other mini-rose growers do.
Repotting a mini-rose Mini-roses don't care much about their pot size unless they're root bound. They stay fairly small even planted in the ground. I have several. Aren't they cute?