If it is that type rose, will the canes eventually provide blooms then?

Yes, but not this year

Your first picture is very lovely. If you have room why not just let the long canes hang down so that they will be covered with flowers next spring?

Sadly, the first picture is not from one of my plants. I grabbed that from the internet to show what I thought my rose might do.

If they don't bloom this year, and I cut them back for winter, then will they bloom next year? The bush is a few years old, but for some reason I cannot remember if the canes ever bloom. I think I'm just getting old.

Are the flowers on your rose the same as the first photo? Do you know the name of your rose. The answer you seek will be determined by what type of rose you have.

Some once blooming roses such as Dr. Huey only bloom on old wood. They should only be pruned right after they are done blooming or you will not see flowers the next year. So it depends on the rose.

I just reread the last part of what you wrote. I'm getting old with ya. You probably don't remember the blooms because the rose was grafted. The grafted variety died leaving the root stock Dr. Huey to grow. Then when you have pruned it your taking off the wood for next years blooms. Don't prune at all this time until it blooms in 2017. Then when it's done blooming prune some it you wish or let it grow for another year.

I don't know what rose it is.

The bottom part bloomed beautifully, and then those canes just started towering above the main bush.