I need advice on trimming my rose bush.

My rose bush grows very long, thick stems that don't produce any flowers. In the past, I have cut these stems back, figuring that they are taking nutrients from the blooming stems. Is this correct? Or should I leave the long stems alone?

Many roses are grafted with a root that is disease resistant and good at getting nutrients, but has poor flowers. The top part is the part with showy flowers.

Long stems, almost like a stiff vine, growing from low on the plant are usually from the root part, and not desirable above the ground. Yours is a bush so the growth you want is the shorter, sturdier branches.
Often the stems, leaves and even the thorns will be different on these 2 parts of the plant.

Dig away some of the soil at the base of the plant and see if you can figure out if it is grafted or not.
If you know the name of the rose, post that, and maybe someone will know.
Post a picture of the plant. Especially helpful would be pictures of both sorts of growth, the long stuff and the more bushy sort. A picture of the base, where it is grafted (if it is) can help, too. Someone can probably look at the picture and tell.

Often the top part will die, but the roots still live. Then the plant will not have any of the bushy sort of growth, just the long ones. If this is what has happened, and you do not want this sort of plant, then dig it out.
If you let it live it can be a reasonable sort of plant where its size is acceptable. One common name might be Rambling Rose. Several different roses are used as root stock, but most are strong, vigorous plants that would become a large mass like a haystack if left unpruned. Some have nice flowers, smaller than most Hybrid Tea or Grandiflora roses. Often in clusters.
Google some pictures of "Climbing Blaze Rose" or "Rambling Rose". This will give you some idea of what some of these roots could be if grown out.

Thank you so much! That is very helpful. I have had this rose bush for many years and couldn't tell you the name or type anymore. It doesn't produce flowers every year, but does most years. I will try to load pictures, thought I had with first post.

IF the long straight shoots are from the root area AND the leaves are a different colour, or if they have more leaf, like the real rose will probably have 5 leave's but a sucker will have 7 leaves then you have a problem with suckers forming from low under the soil, these need removed (not by CUTTING or Pruning) this pruning will only help the suckers to put on more growth and probably more side shoots off the cut branches.
If you have to remove any suckers, the way to do it is to scrape away the soil to show the point where the sucker is attached to the root, were gloves as the other thing about the suckers are they have loads of thorns, take hold of the sucker as low as you can, tug downwards and this should strip off the sucker from the root without leaving any part of it's ste3m. remove all the suckers the same way, cover the roots with fresh humus rich soil / compost with a rose feed added at the dosage given on the packet. water well and prune the rest of the rose to allow it to recover, in a few months you will have the proper flowering show you should have.
Hope this helps you out IF you have a Rose being starved of nutrients due to suckers from the roots.
Best Regards. WeeNel.

The pictures look like the rootstock is growing stems. I have seen that sort of loose, open flower and the tall stems on roses around here.

Especially those tall ones in the last (sideways) picture. Are they coming from the bottom of the plant, perhaps from under the soil?