There's some nice choices in your local shop.
I'm not familiar with the Bergara BMR, I've got the B14R instead. The B14r is getting a little (okay, a lot) heavy to hunt with, but is very accurate. If the BMR is anywhere near it's heavier brother, it'd be fine.
I picked up a CZ 457 Varmint recently. Also very accurate with what I've tried so far, on the heavy side with that varmint barrel but not B14r heavy, mine had some nicely made but plain figured wood in the stock. It's probably going to end up the squirrel rotation. Bolt is not as smooth as either the Tikka or Bergara was out of the box, but I haven't shot it enough to break in.
The T1x is also excellent, although the shop lists a lefty there's plenty of right hand out there that should be able to make Christmas. I didn't care for the factory stock as it comes, but the pieces that modify the T3X stocks fit the T1X. The grip and fore end panels you could take or leave based on hand size, but the slippery plastic buttplate on the T1x really kind of annoyed me. The T3x rubber buttplate fits fine, but will increase the LOP by about 1/2". Long term, it'll end up in a chassis and can compete with the Bergara for precision rimfire duties. With the factory stock, it'd be my pick to hunt if I didn't have the 457.
Savage.... I have several Mk II Savage rimfires. I haven't checked out their B22s yet, perhaps that fixed some of their issues. The Mk II can be accurate with the right ammo, but none of mine are anywhere near as refined as the Tikka, CZ or Bergara's are. Action can be rough, the MkII magazine kind of sucks, bolt handle short enough that about 10% of the time my thumb will turn the safety on cycling the bolt. These things can be fixed, to some extent; and the Savage's will shoot - with the right ammo. But if you have other choices, I'd go with those. I love Savage, they're in my hometown, I've got a bunch - but they are not in the same class.
Haven't used or seen the current T-Bolt, and mine is from 1967 so I don't know how much has changed. The straight pull bolt is just fun, accuracy is good on the old one. My old one is on par with the Savages for accuracy. If they had a lefty in that maple stock, it would go home with me.
Ruger didn't make lefty 77/22's and hasn't made lefty American Rimfires that I've seen. If they ever go LH, I'm in just because I've been pining for a lefty 77/22 since they came out.