You clipped off the first and most important part of my quote - It's your brush. Treat it how you like.
Here's my 2¢. Having done a bit of woodwork over the years, I'd say if it's a wooden handle - tips down. Water is wood's enemy. Quality watercolor brushes typically should dry flat to prevent all kinds of damage usually to the shape (probably not a big issue for shave brushes) and handle. Allowing it to act like a sponge will just encourage cracks over time. You might not see it drip, but shaking the brush gets most of the water out of which the rest of the water evaporates before it gets to the ends. Now plastic, rubber, or metal handles - do what you want. Either way is probably fine.
Here's some food for thought: If you're air drying the brush, most of the water is going to evaporate, not drip off. So.. - If you do handle down, brush up, the water evaporates up into the air in the room and off of the brush/handle. - If you do brush down, handle up, the water evaporates up to the handle where it will condense and drip off, likely back to the brush, repeatedly over and over, a little less each time. Like Kilgore said, I kind of have to think brush bottoms are flat for a reason.
I think the key is air circulation. If the glass has no access to air or air movement, it might take a long time to dry and never if in a vaccuum. As long as you sling water out of the brush after use and/or pat dry on a towel, you should be ok with bristles up drying.
I've done both, hanging my brush from a stand and setting it on the counter and they both seem to dry in an equal amount of time. I like to hang the brush & razor I've just used on a stand mostly to tidy up my counter space in my small den, the others are in the medicine cabinet once dry.
OK got to correct this. First off the glass (or brush) in a vacuum would dry ALMOST INSTANTLY! This is because the rate of evaporation depends on the relative humidity of the air surrounding the hairs. The lower the rh the faster it would evaporate. In a vacuum the rh is 0% and the water vapor is free to move and fill the vacuum. With the upside down glass there would be minimal air movement and the air would become saturated (100% rh), and since water vapor is lighter than air the water vapor would be trapped and evaporation rate would be limited to the rate of diffusion into the surrounding atmosphere, so it would dry more slowly than an upright glass. The rate of drying of your brush would depend entirely on the rh of the room and how quickly the humidity surrounding the hairs diffuses into the atmosphere (the more air movement the faster it dries). The moisture in the knot itself will migrate from wetter to dryer areas. So as long as it is in a well ventilated area up or down should not matter.
When the brush is new and i want to break it after the shaving i let it dry upright I feel that will help the bloom procedure a little bit more.
I have a synthetic brush so I guess that for me it doesn't matter much which way I hang it as it dries quickly and there isn't anything to rot. The reason I do hang it bristle down is because I made a cool rack out of a bent coat hanger that I have been using for 3 years ... I like my weird little hanger so bristle pointing down it is.
They forgot to mention that there must be a little heat below to help the evaporation In a dry glass especially in the country where the water is "hard" after a night you can see the white marks of salts in the bottom. That gives a bad looking and as i am thinking of it i don't want them in the base knot of my brush.
I was talking about a drying rack on the counter - no extra heat underneath, just room temp. The inside of the glass still dries. I see your point about hard water.
Might be a little tight in the den. But it gives me an idea... I know some folks are using old rubber stamp holders to hold their brushes. How 'bout hooking a motor up to one and gearing it up so you can spin dry your brushes!