Well, I guess the first thing I should do is not shoot it too fast. The barrel gets hotter than hell after a few shots.
I know nothing about bedding. It sounds like black magic to me.
As for cleaning the barrel, should I clean it for copper? Because it’s clean as far as carbon fouling and such.
I always go for the cheapest/easiest solution 1st.
1. I check to ensure everything's tight with the scope and mounts.
2. Unless you're the original owner, I'd pull the barreled action out of the stock and make sure somebody hasn't "fixed it" already and the torque the action screws to about 35" Pounds.
3. I'd give it a good cleaning with a copper solvent. I normally use something like Butches Bore Shine first to get the carbon fouling out, dry the barrel completely, then Sweats 7.62 to get after the copper. Follow the instructions! I never go for completely clean, "light blue" is OK by me.
Then I'd retest, first taking a couple fouling shots, then test for groups at a semi-leisurely pace not letting the barrel heat up. I'd even try factory ammo to eliminate an issue with my loads, off the shelf factory should do better than 3MOA.
4. Check the size of your TGT in relation to your magnification and reticle size. With Lower power scopes I've gotten better groups with larger TGTs. IF it is a really low power scope, I've gone so far as to swap out to a higher magnification scope during load development. Then I zero for the load with the scope I intend to hunt with.
5. Don't take this wrong, but try handing the rifle to someone else. Sometimes I find a rifle that just doesn't agree with me.
IF it's still having issues and the rifle wasn't something I bought new, I might even have a smith look at it before I messed with the bedding. It could be an issue with the barrel/crown that no amount of bedding is going to cure. 6mm Rem is a pretty hot cartridge with varmint weight bullets, my 70 grain loads were doing 3600+ FPS and there could be some throat erosion going on depending on how often it was shot and how well maintained.
Also, it's not unusual for lighter barrels to require some pressure up front, which is why you see some stocks with "pads" towards the end of the forearm. For example, Rem M7s come with pressure pads up front due to the light whippy barrels they put on them. Sometimes removing the pressure pad just makes things worse and sometimes adding card stock to increase the pressure makes things better.