Let's go back to the basics .... bedding barrels started back when Mil-Surp rifles were sold to the public then were "sporterized" to get rid of the military look. This technique was very popular with rifles such as a US Springfield '03, German Mausers, and other bolt action military rifles. Military stocks were designed with long forends and heavy stocks to dampen barrel harmonics and make the rifle more accurate. Also keep in mind ... these Mil-Surp rifles fired GI ammo that were loaded with the same specs and bullet weights. Once these barreled actions were installed in sporterized stocks, accuracy typically took a nose dive, especially when fired with a variety of commercial ammo.
The concept is very simple ... if you can prevent the barreled action from moving in the stock and you can prevent the barrel from oscillating (barrel harmonics), the muzzle will predictably maintain the same position when the bullet exits. So when the muzzle is stabilized, accuracy will typically improve. However this is not without issues .... bedded barrels typically get "ammo fussy". GI issue stocks did a very good job of maintaining muzzle stability and even though they weren't match grade barrels, they shot pretty darn good ... due in large to shooting the same ammo.
Shooters learned if you bed the barrel channel so the barrel made direct contact with the stock from the chamber to the end of the forend, accuracy would usually improve. Bedding techniques only work well if the barreled action had a "lug", which is a solid chunk of metal that extends downward from the point where the barrel connects to the receiver. The barrel lug is embedded in a slot of the wood stock with the purpose of keeping the barreled action from moving when the rifle is fired.
Remington, Winchester, and other companies stayed with the military barrel lug design in their sporting rifles but Ruger made a vast change in their M77s. Instead of a "straight down" barrel lug, Ruger made their action with an angle in the rear that mates with a complimentary angle in the stock. This is a very strong design that helps prevent stocks from splitting but it doesn't prevent the barreled action from moving in the stock when fired. As such, M-77s are not as good of candidates for barrel bedding as other brands with a straight down barrel lug.
In years past, I bedded a lot of rifles to include several Ruger M-77s. In some cases, M-77 accuracy was improved .... but only when the groups were poor with the factory stock. In most cases, accuracy was about the same ... maybe a little better with some loads, maybe a little worse with others. In a few cases, accuracy actually got worse .... namely when factory stocked M-77s were shooting groups under 1.5 MOA.
Sundown Thursday, So in my opinion, you risk an irreversible change in your stock that may or may not improve accuracy .... and if it does improve accuracy with one load, it may be dramatically worse with another load. Considering a "field grade" Ruger M-77 rifle was not designed to be a mouse ear accurate target rifle, your silver dollar sized 100 yd groups are very acceptable, especially with factory ammo. Chances are if you reload and take time to tune a load for your gun, you will get even tighter groups.