Discrete glass bedding will help. If your stock is impregnated with preservative in the ways you may have problems getting the bedding to adhere.
If you find your rifle is having accuracy issues once it heats up, you have two options. One let it cool down. Shooting any rifle quickly for a sustained time period is detrimental to the bore and seeing as you aren't shooting under stressful conditions you might as well be nice to your rifle. Two, if you are talking about opening patterns after 3-5 shots you may have bedding issues at the receiver but more likely along the barrel channel. Disassemble the rifle and using a candle, blacken the outside of the barrel all around. Then, very carefully reassemble it so the barrel doesn't touch the fore end of the stock other than the forward pressure point. Take it out to the range and shoot it until the group starts to open up then shoot a couple more rounds so you have a good black mark on the wood where the hot barrel has caused it to warp and come into contact. Very carefully disassemble the rifle again and with a dowel and coarse sandpaper clean up the offending areas. Repeat this procedure until the assembled rifle settles down. Be very careful not to sand off the fore end pressure pads that are there on purpose.
About ten years ago I witnessed a couple of groups fired by a fellow that had sporterised a nice hex receiver Mosin. He had picked up the rifle and the factory sporter stock form International back in the early 90s. The rifle was already assembled as a sporter when he purchased it. Somewhere in the US he had found a strange looking scope mount that was attaché both to the side of the receiver and on the top flat. It was cast iron and very nicely done. The scope was an old K4 Weaver. The rifle still had its original length bbl. When he was finished shooting some very decent groups that were about 1.5 moa with factory Norma ammo I asked if I could look over his rifle. He was a very nice fellow and handed it to me. It had a beech stock with a pistol grip and the fore end went past the tangent sight about 12cm. The stock was about as plain as they come without checkering. The one thing that was notable was that it was free floated from about an inch from the receiver. By the way, the bore on this early model 91 was almost perfect. It shot very well.
All of my Mosins, Russian, Finn, Westinghouse, Hungarian, Chinese and Sig shoot very well as is. Especially the Soviet 91/30s with laminated stocks.
The Finns found out early that the Mosin stock wasn't always good and many of their stocks have been assembled in two pieces with finger joints just after the reinforcing bolt.
Considering the age of these rifles I am very surprised at how well they shoot. It is a testament to their builders, often under extreme conditions.