Climbing roses bloom on the canes that grow off the main canes, like what you're referring to as the skinny trunk. You encourage those lateral canes by training the primary canes horizontally, or by trimming off the tip. Since you already have some time invested in that skinny primary cane, you might try just trimming off the top to allow side buds lower down to grow. They won't want to grow downwards, so you'll want them to start from lower down.

Most climbing roses need at least three years to get established, and then they throw out more of the primary canes for you to play with. If yours is more than three years old, and it only has the one primary cane, you might want to try feeding and watering more to encourage it to put out more canes.

If trimming the top, and extra fertilizer, don't do the trick then I vote for B. I don't think A is a viable option, and C should not be necessary.

I did the same thing with a Jacob's Coat -- I wanted to get it tall enough so that the deer didn't eat it -- but it just looks ugly! I've been trying to get it to branch out for a couple of years now with little success. I'm interested in the answers from the experts too.

If you can't get it to grow more bushy, grow some clematis with it. They bloom when the roses don't, and you can plant a shorter one that will cover the "stem".
Kathy

Or plant a clematis that blooms with the rose.

Thanks for all the suggestions. What fertilizer would make it happy and encourage that growth?

You can find products labeled "rose fertilizer" at garden centers. Don't fertilize liberally for years without checking with a soil test periodically, you want to avoid a phosphorus buildup in particular.

You do want to keep them adequately supplied with nutrients, large-flowered roses need good soil to be fully productive - even most wild roses are characteristic of fertile soils in nature.