I have a Savage model 25 having issues with first round fliers. First shot from every group will hit about the same place. Every shot after the first one goes low right and will group about MOA with shots 2-5 or however many I decide to shoot. I can let the gun set for 15 minutes, shoot another group and it does the same exact thing again. It's a 17 hornet with around 800 rounds down the pipe, it use to shoot 5 shoot groups 3/4 moa consistently. I've cleaned the barrel really good since the issues started, thinking it was just dirty but that didn't help. I've checked the rings, mounts, and stock torque. I bedded the action and that didn't help. My bore scope won't fit in the 17 cal barrel so I can't check it out.
Picture is of two groups shot about 20 minutes apart.
View attachment 268620
Your rifle is two grouping. This is due to several issues:
1. Action is stressed (i.e. not bedded).
2. Loose screws.
3. Barreled action sitting on metal pillars.
4. Front screw of front scope base is contacting the barrel.
Rather than make this look like a diatribe, I'll just list what I do when I get by paws on a new or used rifle:
1. Clean barrel.
2. Bed barreled action and free float a couple of inches forward of the recoil lug. It is bedded tight. It only takes about 15in/lbs of pressure to stress an action so bedding is a must.
3. Install bases then check for screw contacting barrel. That entails removing front bases/screws. If you peer down into the screw hole and see a shiny spot or mashed barrel threads, shorten front screw .010 and check again. Then make sure to loctite all screws. 20in/lbs.
4. Make sure any magazine, mag box assembly or bottom metal is not too proud. If so correct.
5. Tighten action screws to 35-40in/lbs. Use vibra-tite by loctite (medium strength) to secure screws.
In your case, start shooting your preferred loads or shot factory ammo if you like. Keep shooting, do not clean barrel yet. Clean when your groups start to go wonky on you.
May seem ridiculous to take this much time on a rig but doing so has kept me from pulling more hair out of my head than necessary. Hope you find the problem so you can enjoy shooting your rig.