Where are you located and what kind of roses are you growing?

My first guess would be that they are not getting enough sun. Roses need at least 6 hours of direct sunlight to bloom and 8 hours is best. Roses in too much shade may grow tall canes trying to find more sunlight.

It also sounds as if what you have is root stock. Those types used to bud commercial varieties on can flower well and are considered attractive by many people, but they are once flowering and usually climbing. What do the flowers look like? Please take a look at the link below to see if yours resemble these. If they do, you have Dr. Huey, a break through rose of its time, but these days, pretty much a museum piece and widely used to supply roots for commercial roses. Kim

Here is a link that might be useful: Dr, Huey

Sounds like the grafted variety has died out and all you have left is the rootstock, root hardy but not stem and leaf; so the grafted top winterkills and the rootstock sends up suckers every year. No flowers because the rootstock only blooms on two year old wood and no tops live that long. This is a very common result in the North Country if hybrid roses are not properly winterized, and sometime even if they are. One thing to counteract that is own root varieties that bloom on first year wood. There are also some that are stem hardy, but they tend to be shrub roses, a little less tame than HT or floribundas, etc.

how do you trim a rose bush gone wild to get flowers

You don't. If the issue is the root stock has taken over and the budded variety you wanted and obtained to plant has died out, then you are left with a once-flowering climber. If you want it to flower the best possible, then you train it as you would any climber, bending the canes down to closer to the horizontal so it produces lateral growth along the canes which will then flower. If you don't want a climber or haven't the room for it, then you simply whack the heck out of it down to about the size you want, then it will flower NEXT year on the remaining growth. Or, wait for it to flower, then whack the devil out of it. Either way, you likely have a once-flowering climber and eventually you're either going to have to treat it like one, keep whacking it down to keep it a small plant or replace it with a new plant. These are Dr. Huey, the likely rose you have and are dealing with. Notice the tall growth above the one plant? All the others would have those, too, had they not been cut off. But, they WILL appear...sooner or later.