I travel extensively, and often need to pack my shaving stuff up to check out of a hotel before my brush has a chance to fully dry. I travel with an inexpensive boar hair brush for two reasons. First, It’s cheap enough that if I accidentally leave it behind at a hotel, it’s easy to replace. Second, boar doesn’t hold water as well as badger, so it dries more quickly.
To aid in the drying of the brush, after I’ve rinsed out the soap and squeezed out the water, I place a hand towel on the counter and dry my brush on it, using a motion just like I’m lathering up some soap. Then I can put the brush away in my shave bag. When I get home, I’ll take it out and allow it to dry fully.