No need to plug the bbl when rust bluing
Leave the crown In-the-White. It'll get a little color during the process, but can be quickly brightened up again.
Leaving it in the white avoids wiping rusting soln on it and chance of getting it in the bore if you are concerned.
Not that it would bother anything unless you let the thing rust excessively.
Same with the flash hole, open.
Wipe the soln right over it and you shouldn't get any inside the bbl. The swab with the soln should be damp with it, not sloppy wet.
The boiling water or steam cycle? Won't do anything to the bore. The metal drys of it's own heat in a few seconds.
If you want to, run a DRY patch down it after the carding. Don't introduce any oil to the process.
If you really want to get excessive you can coat the bore with common shellac and that'll avoid any damage for sure.
I use that on bbls when Damascus finishing and they have to go thru an etching soln dunking. The bore(s) must be protected from that.
Stands up to repeated boiling cycles though I re-coat the bores at about cycle #9 when doing Damascus. It takes more
cycles to complete than a straight rust blue.
I've been rust bluing for over 50yrs,both Slow Rust and Express and have never plugged a bbl when doing so.
That includes everything from a MLdrs to Stevens to Purdeys