I started out shooting 10-shot groups when trying a new load. After a few years, I got lazy and cut back to 5-shot groups. I guess there was an unconcious decision that since I'd found a good load for a .30-'06, the gun would have to fit the load.
In recent years, I just load three rounds of some bright new idea and see what happens. If I can put three shots inside, say, 3/4" with the '06, that's as good as I need. I'm a hunter, not a bench-rester.
The first shot is always from a cold barrel. I'm not in a hurry, but I don't wait around very long before #2 and then #3.
I've never cleaned the bore between several groups of loads. Doesn't seem to matter.
When I'm getting ready for deer season, I'll thoroughly clean the bore. I'll shoot three shots; if #1 was not off from the other two, I'll call it "good". If it's a flier, I'll fire a fourth shot to see if I'm getting a good three-shot group. And gripe; #1 should not have been off...I'll wait til the gun is all cooled down and shoot three more. Usually, that's all that's needed. Sometimes, the first shot from a very clean bore will wander off from where it oughta go.
Absent wet weather, I won't clean the bore again til the end of the season.
Hope all this BS helps.
Art