Here's a good picture of the Ruger #3 showing the barrel shank.
Ruger #3 Shank - slow server here so give it a few seconds to load.
Enlarge the first thumbnail on the bottom left and then enlarge it again for an extreme closeup. It looks to be a straight shank at the receiver and then tapers off in front of the rear mount. That's why I recommended the EGW radius universal mount, although I don't know for a fact that it wouldn't have a tiny bit of forward lean depending on how straight and level that shank is. But since the Fastfire 3 has 115 MOA total adjustment you wouldn't run out of room.
Another way, and one I've done on other rifles, is to get the Weaver rear mount shown in the picture, it's their #85 or 48085, so you'll have a flat, horizontal mounting surface that for sure will fit the barrel contour there and then use the Fastfire's included picatinny base to attach to that. The Burris base will overhang the front and rear a little bit but the cross slot will be centered. Couple that with the big ugly knob Burris insists on using with their picatinny base and it's not the most elegant solution ever devised but it's solid and it works.