In the winter, I will lay it on top of the electric radiator heater. The heater gets hot, but not hot enough to burn you. Just hot enough to be rather uncomfortable if you leave your hand on it. The rest of the year, I hang it in a brush holder.
Despite I believe that holding wet brushes upside down is not necessary, here is an improvised holder made of a Scotch tape holder. I love quick and inexpensive solutions. After you shake water off the brush, the remaining water is held with rather capillary action than gravity. That means It does not really matter whether you hold it up or down, it will dry out with the same speed. Do not trust me? Set up an experiment with identical brushes. Just weigh them every 30 min or so to see whether one or the other dries out faster.
I held my boar brush in a holder for some to see the difference, and it just seems that the bloom isn't so nice when the bristles are hanging upside down But I haven't noticed it being any dryer
I abuse my boars. I just shake them and Chuck them in a shave mug.. My one and only badger gets hung in a brush holder.. does it matter? Don't know. But I do think it looks better.
For your boars - handle up or handle down? I ask only because I've seen many vintage boars with permanently bent over bristles, obviously left bristle down in the mug. But, hey, they're your brushes. Treat 'em how you want.
I have a Muhle boar brush which has been used for 21 years. I always left it on the shelf with the bristle up. Although it lost probably 20% of its bristle, it still looks pretty good and might serve for another 21 years, but I retired it and will use new ones.
Usually bristle down. like I said I know it's abuse. This would be akin to saying "but she's fat and ugly" in a domestic violence charge but it's an $8 brush. If it's any consolation both of my boars are still straight and have in all likelihood became shelf decorations.
I have a stand that I made from some 6 gauge copper wire from lowes and a piece of wood that was actually meant to be a Plaque that hangs on the wall I got from hobby Lobby for like 80 cents. I think the entire stand cost me like 4 bucks.
I give my brushes a good shake, gently 'strop' them on a clean dry towel to remove most of the remaining moisture, then hang them bristles down. I shave in the morning so once I come home from work, I give them another strop to fluff up the bristles, sometimes give them a combing, and then stand them on their handle until the next morning when I hang them in the brush closet and choose that days brush.. Repeat the process
