I have actually seen both phenomena in my bridges. Mostly, they bend upwards, that is with the top of the bridge curving towards the fingerboard. This I think results from not checking each time I tuned that the bridge was still absolutely vertical. That's what is going on with my bass now, but it is really mild, and I probably will live with it a while longer.
The downside of doing the steam treatment is you have to take the bridge off the instrument, and make sure it is good and dry before you use it again. That might mean a week or two of no instrument, unless you have a backup.
I have had a bridge on the Satanic Cello bend downwards, towards the tailpiece, and I have no good explanation for why, nor does my luthier. An inherent flaw in the bridge itself is possible, or just having the thing go a little out of vertical one way or another, and the strings exerting such tension that the bridge cannot withstand it and starts to curve. Once curving starts, it accelerates, by virtue of the forces of the strings no longer being supported by a straight column of wood.
The cello had a Belgian bridge on it when I got it, which if you research is intended to support the high registers, and provide a brighter, louder sound. But they are designed differently, with longer legs and a smaller body, thus a bit lighter and more likely to bend.
Because that cello didn't really need the boost, we changed to a regular French bridge, and when the sucker went on to bend a couple of those, got a "special" bridge blank of even harder wood than is typical. I am not sure of the details, but know that it cost more.
We shall see. I really like the strong/stark strings with max string height, so I may be making my own trouble. But I love the cello, so what's a girl to do?