Put it in the coolest spot in the garage you can. Maybe a friend has a cooler garage you could use. Sometimes a greenhouse or nursery will baby sit your rose for a fee, and let it have Spring early.

Do you have a lot of windows? Maybe blocking out the light would slow it down.

First, what do you mean by budding out? A lot of roses start to push buds during the winter, but only go so far. So a certain amount of it is normal. Second, what is the usual temperature of the garage? Proper storage temperatures are around freezing, but that is difficult unless the area is temperature controlled. Generally, though, you want somewhere that is going to be below about 40.

Thank you, it has been between 40 and 50. I have about three inches of new growth with tender new leaves on the plant. I reduced the temp to below 40. Should I leave the new growth or prune it off?

What part of the country are you? A pic of the plant would also be helpful.

My tendency is to say prune it off at proper pruning time for your zone. There are folks who live in zone 9/10 where roses never really go dormant, and come early spring they do a heavy pruning, new shoots, flower buds and all.

This is happening to many of my outdoor plants also, so I'd advise just let the new growth takes its own course.