Rugers generally don't have seperate bases like most other guns, but rather have the receivers machined in such a way that you attach Ruger-specific rings directly to the rifle. Pretty nice system IMHO (though the only Ruger guns I own myself are a 10/22 and a P95, so I don't own anything that uses the Ruger system).
Now, Burris does make rings that attach to the Ruger system, but it doesn't look like they make their signature series rings like this (it looks like it's basically their regular Zee ring).
You also have the option of getting an adpator to go from Ruger-style rings to Weaver-style, but this doesn't seem like a good option IMHO. Just 1 too-many clamps in the system.
Personally, I'd say the best choice would be to get a set of the regular Burris rings made to attach to the Ruger mount system.