I planted a New Year rose bush in early April. It is growing beautifully. It has a cane that is almost 6ft tall standing alone. It has another cane that I have trained along a rail and it has produced shoots 3 feet tall. All that said, I have yet to see a bloom.
You planted a climbing mutation of a bush rose. It’s attempting to grow to its mature size and should begin flowering once it has produced the root and foliage mass it requires to produce them. The plant looks great. I’d continue training the canes out along the railing so they produce lateral growths from them, which will then flower. Otherwise you will have flowers at the top ends of those long canes instead of a long cane full of flowering stems.