Burris rings, Leupold mount?

[Sabre]

I'm looking for a mounting system to perch a new Bushnell 4200 on top of my Savage M10. I like the Burris signature rings but not their bases. Will a Burris ring fit solidly into a Leupold mount?

In a word--Yes.
The Leupold bases will work with the Burris rings, but I recommend that you use the Burris Zee rings, which are Weaver style, and the Weaver style bases of your choice. The "Standard" style base/ring system is just not solid enough to hold a heavy scope on a hard recoiling rifle. I have seen the windage adjustment screws back out and have even seen the dovetail sheared off the front ring under recoil. If you don't like the Weaver style, at least get the Dual Dovetail setup.