No worries, you just have blind shoots. As long as you supply your roses with full hot sun, and look after them properly with water, fertilizer, mulch, etc., they will bloom.
The reason for blind shoots is poorly understood.
Paul Mozarowski.

Should I cut back the blind shoots this winter like I would do with most roses or let them be?
Thanks for the advice!
Michelle

The last time I looked it up, I don't think there was any specific advice. I might be tempted to peg them down to encourage vigorous side shoots, just to see if that does the trick. Paul Mozarowski.

What you describe is common, particularly when growing climbers from cuttings. If it is a climber you are growing, do not prune except for dead wood/ tips after winter for the first 4 years or so; they resent it.
Otherwise, what Paul wrote.
Steve.