It will be one of the best 22's you ever bought or a looser. Don't get me wrong, I am a Remington fan. I own several different Remington 22's as well as other makes.
The 541's were a hit and miss situation. Some shoot absolutely great out of the box. Others need to be bedded. And still others you can spend as much as a a 40X would cost and still not have a good shooter.
One thing some guys do is to have the action threaded and thread the barrel and rechambered.
Some weld a tang on the back of the action to add a second action screw for better stability.
Using a inch/pound torque wrench torque the action screws to approx. 15 in/lbs. Start at 10 and go to 20 or so and find the sweet spot where the rifle will group at its best.
I gave up and sold mine 541HB and bought a 581 and started with a new target barrel. The action was trued and threaded, threaded the barrel with a match chamber. I put a 540XR trigger on it and still ended up with a so-so shooter.
Be patienct and try one thing at a time to find what works. :wink:
John