First-off, if you're finding too many grouse, please PM me. I'd be more than happy to help, and the ammo is on me.
To your question~I only own bolt-actions .22s for 2 reasons.
#1. I've never shot a semi (out of the box) that can compete, accuracy-wise, with an out-of-the box bolt action, period. The only one that I've heard promising things about is the Thompson R-55 but even then, I don't consider that a field/carry rifle. I've also read that it's fussy on which ammo it'll shoot well. Savage and CZs bolts are what I have the most experience with, but I've owned Winchester levers, a Ruger 10/22, etc.
#2. I like to keep my rifles clean so that they'll function well and look good when the rare opportunity to use them comes-up. Bolt actions are WAY faster to clean because you don't have to take the damned things apart to do it. And no screwdriver involved.
So, like any gun purchase, I think it's a matter of setting the criteria based on priorities. Fastest follow-up shot, sounds like you need a semi. Quick follow-up shot with superior accuracy, bolt-action repeater. Great accuracy AND the ability to feed it the widest variety of ammo~bolt-action repeater, w. tubular magazine. Most can digest S,L,LR. Assuming the sky is NOT the limit budget-wise, these would be my choices buying new today;
Semi~Marlin 795 Very inexpensive, very light, inexpensive magazines and available in stainless for a few dollars more.
Bolt-action~Savage Mark II, I like the BV with the heavy barrel and laminate stock, but standard-weight barrels would be a better choice for offhand shots.
Bolt-action tube-fed~I'd be looking at a Marlin XT-22. Supposed to be pretty good rifles, and definitely inexpensive.
Good luck, the research is part of the fun!