Arabella maybe? Do you prune the burning bush to the ground every year? Selectively prune older stems to the ground every year? Maybe you should let the bush go for a couple of years and then prune it to the ground and it wouldn't be so bare at the bottom.

One of the challenges for that pairing is root competition. BB has vigorous roots, so you will want a Group 3 clematis that is a strong grower. A few that come to mind are Prince Charles, Ville de Lyon, Polish Spirit. And Jackmanii is always good. You will also want one that is mature. A 2-gallon plant should have enough roots to get off to a good start. Anything smaller and the roots may struggle in that bed. Make sure when you buy it that the pot is mostly roots and not mostly dirt!

The other challenge is placement. You can't plant it too close to the shrub -- again for the root issue. Normally I would say plant it outside the drip line of a mature or almost mature plant. But if you are pruning the shrub regularly, it is hard to say just where the natural drip line would be.

fwiw, I pruned 3 BB's severely for about 10 years and finally gave up and just removed them. They can take a very hard pruning, but it was too much work when I had better things to be doing in the garden. Mostly I pruned them to avoid flower production to keep the seedlings out of the woods. It was not completely successful.

Thank you for your suggestions.

Thanks Wendy for saying what needed to be said.

Arabella is a good choice as it stays small, although it is nonclimbing. Prince Charles and Polish Spirit are huge clematis, correct? I don't think they would work.