I never tried a dry patch first. Here's how I do it.
I use Butch's Bore Shine.
I run a soak patch of Butch's down and flip it over and down again.
I repeat with another soaked patch. Let it sit for 1 minute.
Then 3-4 dry patches and the bore sparkles.
A patch of Break Free to protect.
Then I twist an 1/8" drill in the flash channel, and then soak the BP in a small tub of Butch's for 10 minutes.
Then wipe off the BP and install with no lube on the threads. It's not needed with BH 209.
Right before shooting again I run two dry patches in the bore to remove the Break Free.