The rimfire Bisley is an attractive gun. At 43 oz, I found it to be rather heavy for a .22, with its thick, 6.5" barrel.
(Note that the blued Bisleys have steel grip frames, unlike blued regular Single-Sixes, which use aluminum grip frames. This adds weight to the Bisley version. All stainless Ruger single actions have steel grip frames.)
The 5.5" stainless Single Six is no lightweight at 39 oz, but for a .22, it'd be my choice over the Bisley. Handier gun. You will appreciate those four missing ounces, trust me.
Also, Ruger leaves the sides of the hammer on its blued single actions "in the white" - they are unblued, plain steel. This draws rust. The stainless steel gun will let you avoid that problem.
And yeah, you get a bonus .22 Magnum cylinder with the stainless Single Six, but not with the Bisley. That may be important. Here is why. All Ruger's single action .22 revolver barrels (except for the Bearcat, I think) are actually cut to accommodate the .22 Magnum bullets, instead of the slightly narrower bullets of the .22 LR. I dislike this setup -- I wish Ruger would scrap the whole idea of the "convertible" Single Sixes, and either drop the .22 Magnum chambering, or sell separate .22 LR and .22 Magnum versions of the revolvers, with barrels cut separately to the right diameter for each caliber, improving accuracy. But as it is, you should get the convertible -- maybe your gun will shoot tight with the .22 Magnum if it doesn't shoot well with .22 LR.
Me, I want a rimfire revolver to accurately shoot .22 LR, period. I was not satisfied with the accuracy of my .22 Bisley, so I sold it. It was not nearly as accurate as my S&W 617 double action .22 revolver -- even with a shorter 4" barrel on the Smith -- at least in my hands.