All my .22LR rifles that came to me equipped for mounting optics, except for one, a Savage that I had some years ago, have had dovetail grooves, some of them also drilled and tapped for bases. I have used dovetail rings when possible, except for Burris Signature Zees and delrin dovetail to weaver adapters on several sporters. If I recall correctly one of those rifles with which I used dovetail rings had the dovetail grooves (or the barrel) out of alignment to the point where I had to adjust the windage almost all the way for shooting at 50 yards.
I suspect the holes on your Bergara are not perfectly aligned. But as suggested by someone above, it's often worth switching the bases, front for back if possible because the bases may not be perfectly true.
If that doesn't help and you have
Burris Signature Zee rings, the ones that use the delrin inserts, including offset inserts for elevation and windage adjustment, you can set them up so that you can use your rifle without issue as is. The inserts come in pairs of +/- .005", +/- .010", and +/- .020" sizes and you can use them in combination to move the windage and/or elevation considerably, by as much as 24" at 100 yards. (Note:
Burris Signature Zee rings use the inserts, Burris Zee rings do not.)
If you want to try the Burris Signature Zee rings but can't find the offset inserts let me know. I have an extra set.