+1 what snyder says. I've done hundreds of bbls and parts and other than doing damascus bbl finishes, have never coated the bores.
The rust blue soln that you're using will disolve off of the rusted bbls and parts & into the water in the tank.
You have to keep that in mind. Some are more corrosive than others and the boiling temp of the water can aggrivate the situation.
It's usually never a problem if the bore(s) are wiped clear when the bbls are taken out of the tank.
I just use plain clear hot water dampened patches down the bore(s),,a couple each after the carding and before the next coating to clear out any residue so it doesn't sit in there over the next rusting session..
The effects of the diluted rusting soln in the tank water is easily seen in placing a polished piece of steel in the water while doing a quick rust blue job. With out ever placing any blueing soln on that polished piece and just letting it sit in the water while you go about rust bluing another project,,it will take on a very nice deep gray color that can be enhanced and evened out by occasional cardings right along with the rest of the parts. It's being etched by the tiny amt of ferric chloride (or what ever other corrosive chemical) is in the bluing solution.
If that small steel piece was taken out of the tank and allowed to sit untouched,,it will rust just like a shotgun or rifle bore will even though it never had a coating of bluing soln applied.
Dunked into and then taken out of and dryed,,then wiped clear of any reside with clean water water,,it'll remain unharmed. Perhaps a bit discolored,,but easily brightened up like the bore with w quick pass or two with the right brush.