I just installed a Ruger factory Bisley gripframe on a NM SBH. Here's my story. (By the way, I need to add that I don't know whether the OM cylinder frames are different from the current NM frames, so I'm not sure the parts will bolt up at all -- can't help you with that one.)
First Bisley gripframe had was an incomplete casting at the top, where the grip panels meet the frame. Oops.
Second gripframe had holes drilled in a position that caused a significant misalignment between the gripframe and the cylinder frame. Oops two.
The third one was OK on the sides and complete all the way around, but...you need to understand that the angles of the cylinder frame on the Bisley and the BH/SBH are not the same at all. The rear of the BH/SBH cylinder frame is a sharper arc. Getting the two to match will usually require removing metal from both parts if you want the arc to be the same where the gripframe meets the cylinder frame.
There is a good little narrative in Ruger - The Man and His Guns on the Bisley development. Ruger tried to do the Bisley using the existing BH/SBH gripframe, but couldn't -- in the end they had to manufacture a separate, different, cylinder frame for the Bis.
There's a very good discussion of the fitting process in Kuhnhausen's book, but it's mostly pretty obvious.
The parts for the full conversion are not cheap...maybe $200 retail. You might just consider buying a Bisley...?