Ballistol is basically a mineral oil base with some long chain alcohols added. It will not evaporate or dry readily so soaking a piece of patch material in Ballistol and then trying to dry it is like putting oil on a rag and expecting it to dry. The drying process that you ate talking about is for folks who dilute their Ballistol in water, wet their patches and then dry out all of the water. Many like to do it that way but I use straight Ballistol on my patches. I pre-cut them and put them into a large pill bottle from the pharmacy. I add a bit of Ballistol to the patches and turn them a bit to get all of them wet. Then I let them sit in the closed bottle for several days to allow them to be come evenly moistened by the Ballistol. Lastly, I remove all of them from the bottle, carefully stack them and use my finger pressure to squeeze any excess Ballistol out of them back into the bottle. Any Ballistol in the patch bottle will be poured back into the original Ballistol bottle for future use. I return the patches to the medicine bottle and they are ready for use. If you use all of your finger pressure to squeeze the patches, they will then have just the amount of Ballistol left on them that you need. At least, that is the amount of Ballistol that I have found to work best for me and keep the fouling to a minimum.
As a dry lube, one of the leading experts on muzzleloading accuracy, Dutch Schultz, swears by it. I am less fond of dry lubes but that is just me.