10M air rifle benchrest help?

I haven't heard about anyone bedding a FWB 300S, but I would advise against it because you may ruin the recoiling sledge action. I shoot my 300 at 25 Meters using JSB 7.87 gr pellets, and I must say that this gun is difficult to beat. At 10 M, I would use a quality match grade wadcutter pellet like RWS 10, RWS Meisterkugeln, or H&N match. Probably the lighter weight pistol version, but you need to test them. You need a SOLID table and develop your technique. I never touch the gun during the firing cycle to avoid undue pressures on the stock that may cause the gun to move when the shot goes off. Just put your finger on the trigger. Some folks put their thumb on the backside of the trigger guard and pinch the trigger with their forefinger.. All good things to try. If I can do this at 25M, you should be able to get a 250 all the time indoors at 10M.

I would underscore what JPS said. "Develop your technique". Meaning, keep shooting over and over until you can do it exactly the same way. Not sure how much you have shot, so you may know this already:

Remember to follow through with your shot. When the shot breaks, leave your trigger finger just as it is. Don't move it at all until the pellet punches the hole through the paper and you can see where your cross hairs are. If your cross hairs are not where they were when you were taking aim, then you'll need to adjust your technique. 

Have fun. Practicing and getting better is the best part!

Chas

Sounds like great time... Best of luck!