I'd prune it hard in early spring - late February or early March. Fertilize at that time as well.

Depending on the type of rose, it may well have a growth habit that tends more to tall and lanky rather than short and bushy. Using alfalfa meal or alfalfa tea will encourage basal stemming and that can contribute to a fuller, more bushy appearance.

I prune mine when I get around to it. I don't think there is any problem doing an earlier cut as long as the rose is already going into dormancy. Cutting too early does risk triggering a flush of growth which will inevitably get whacked by frosts...but once November comes around, I start cutting back as dealing with 100+ large roses* is not something I could easily accomplish in a few short spring weeks.

*Down to a more manageable 60 or so...but I still do the pruning throughout the whole winter (because there are all the fruit bushes too).

I'm with Vapor. What is the plant's name?

If you just transplanted the rose, I would leave it alone this fall and mostly just focus on watering it as you go into the winter so it has a strong root system. Then you can look into a hard prune in the spring (maybe cutting all the canes down to 6" or so) to see if it bushes out better. The main exception to that is if you have a once-blooming rose (like a Gallica or Alba), because you'll cut off the season's blooms, but if you bought the rose at a store like Home Depot or many garden shops, that is not the most common type of rose sold.

Remember that any rose will build stronger canes with time and may take a while to settle into its final form for the bush. Also, some roses like to grow broadly or lanky vs. bushy and will resist reining in with pruning. If you take pictures of the rose when it blooms we may be able to help you identify it and give you more specific advice.

Cynthia