Prolly won't win points for this, but I doubt that I'd opt for a .22 LR pistol as a bug-out gun. The paucity of ammo on shelves disinclines me. Could I scrounge some from an abandoned home somewhere? Who knows? The "abandoners" probably would have the sense to take any firearms and ammo with them.
I'd likely go with my Rossi M1892 lever action in .45 Colt, with my Redhawk in .45 Colt as a sidearm (not the lightest nor most concealable combination, I'll grant you). I'd want a more powerful rifle round for places where bear or game larger than mule deer are likely.
If longer range, concealibility and weight are salient considerations, a bolt-action .308 and my Ruger Police Service Six would probably be my pick (there's ALWAYS something that a .38Spl/.357Mag can fire, laying around, somewhere. At least there was, when I found no 9mm on the store shelves).
If not the Ruger .357, then probably my Springfield M1911A1 National Match, with my .460 Rowland conversion tucked into my backpack, plus the same bolt-action .308, or my M1A.
If I HAD to find something to go with a 10/22, I'd probably want a J-frame S&W with adjustable sights and if possible, an interchangeable cylinder in .22 Mag. Fulfills the weight/concealability constraint. Just leaves the person bugging out a bit light on power.