I've shot a lot of BH from production rifles in the past. I've never had a rifle that would shoot to POA with a clean barrel. Most all my rifles required 2 rounds before the POI and POA became the same. There are a lot of concoctions people have came up with which they say will bring the first shot to all other shots, but I've yet to find anything that works, short of fouling the barrel. My normal practice was to swab any lubricants out, fire two primers only, then send two rounds into the berm on my range. After the second round, I loaded the rifle for hunting. I never knew rather my first hunting shot might be 35yds or 250yds, so it was necessary my POA and POI were identical. Unless the rifle was exposed to heavy rain, or a lot of moisture, it would remain loaded for up to two weeks. If I had any doubts with moisture, I'd fire the round and reload it.
Some rifles want to be swabbed between rounds, others you can shoot 50 rounds without swabbing between shots.
Although BH is less hydroscopic, it can still corrode. I've never had a problem with corrosion myself, but your mileage may vary. When in doubt, clean it out.