I am in California and it's not terribly humid here either. I clean bp fouling with tepid/cold water, then use WD40 and like Daryl, I have never had a rust issue even after longterm storage. The only rust issue I have had was when I tried hot water and got a little flash rust after a day or so. Another thing that slows down cleaning and encourages after-cleaning rust, is mixing oils with fouling before cleaning. But that is my experience and might be different for other locations.
BP fouling is very easy to dissolve with plain water when the fouling is mostly free of oils. if oil or oily solvent is added to the mess, it takes me three times as long to get rid of the fouling, and I will often need to add an oil cutting dish soap like dawn to the cold water, to help out. If I keep the fouling free of oil, I don't need the dish soap.
After the water comes out clean, and the patches are free of color, I run a dry patch, and then WD40 soaked patches down the bore. I will check the gun after a few days, and sometimes run a patch or two of WD40 down the bore again, but not always. I can let my guns sit for a year- even 2 years that way, and when I check the bores, they are free of rust usually.
Another issue I found was the difference my lesser used bp guns handle fouling and rust compared to the guns I use more often. The newer gun gets fouled more and rusts more when out in the field. I have found that the more I use and clean the gun over time, the easier it is to clean and the better they handle bp fouling and less rust occurs. I know some might define that as "seasoning" but I don't. I interpret that as a result of "burnishing" the bore with regular use. I have no scientific support for that, just seems to be that way.
K
I have used Lehigh Valley Lube, Ballistol, ATF, and WD 40 and found that all 4 work about as well as a rust inhibitor. I settled with WD40 because it was already in my house and easy to get.
Ken