After you've done what Gairlochian said, do you have a know proven-good scope you can switch over to?
Remember, just change 1 thing at a time to narrow down the problem.
After eliminating the scope, rings & bases (including ensuring the scope base screws are not too long & hitting the barrel threads), start looking at your rifle.
Are you letting it cool down between shots? Is it a mild calibre or a boomer? I can go 10-12 shots in my Hornet before I can detect any barrel heating, unlike a pencil thin .30-06 barrel, or a .30-30 that start tossing shots after 3 in a row. No longer have a small calibre magnum rifle, but when I did, anything more than 2 shots out of my .308 Norma would open up a group & heat its barrel.
Can you slip a sheet of paper around the barrel & move it from just behind the tip back to ~1" or so in front of the receiver? Even better, is there any rubbing against 1 side of the barrel channel?
Has your barrel/action ever been bedded or replaced in a different stock?
Is it a new or new-to-you rifle, or have you never had this problem before with this rifle?
There are a whole lot of things that can go wrong!