...
Bore snake right after the last round fired.. while the barrel is hot.
The only time I scrub a barrel is IF I see copper build up or some kind of burnt powder contamination (thru my magnifying lamp).
For the interior protection of the barrel, from rust, I simply run a pad with a "very light coating" of EEZOX, let it sit for half an hour, then run another clean pad thru it, lightly, to soak up any over-kill.
Been working fine with 5 pistols over the last 2.5yrs.
Forgot to mention: and for the 9mm's I use a 40cal bore snake. For the 40 S&W's I use a 45cal bore snake and for the 45cal gun, I use another 45cal bore snake..
OMMV,
Ls