Every revolver is different, so without a lot of experimentation, it's difficult to predict if your Bearcat is super-accurate, or maybe not so much.
My experience is they can be quite accurate, but they're not always easy for just anybody to shoot well. Rudimentary sights with a tiny little grip requires a lot of practice to learn to shoot these revolvers well, and to precisely duplicate your shooting discipline shot after shot. I'm not being condescending, as this also applies very much to me.
Over and above this, the condition and size of the bore and cylinder chambers can very much dictate which ammunition your revolver might prefer. A CB or other short also just might not obturate enough in your barrel to get duplicate velocities and duplicate bullet stabilization.
A new barrel can have millions of microscopic imperfections that get smoothed out somewhat by continual shooting and cleaning. These cleanings can also remove lead deposits that can have an extreme impact on accuracy.
Don't give up. Keep shooting this revolver. And try some different ammo. Maybe lots of different kinds.
Now for a little story. One particular Single Six I own, from the first time I shot it, I was horribly disappointed with the accuracy. I bought a Paco Kelly Accuriz'r tool, and enlarged the bullets slightly on my .22 ammo. It made a huge and immediate difference. Then thru laziness, I used this Paco tool less and less, and finally not at all. But... For whatever reason, this revolver now shoots extremely well with most out of the box ammo. There are always exceptions.
Was it the many cleanings that fixed this gun, or the deposits, copper/lead/lube, filling the imperfections?