First up, I do not grow begonias so I could be wrong about all of this. But, I am considering this particular begonia because you can turn it into a bonsai, and I've done a bit of research. My understanding is that it prefers to dry out between waterings. This can be done in a terrarium, but you would pretty much have to change the potting medium. You definitely want to avoid rotting the tuber from too much constant moisture. It also needs quite a bit of light - another difficulty under glass because you'd get a lot of evaporation and condensation. (It might be fine until the summer.) It will need pruning to stay small. I guess none of this says that you couldn't grow under glass, but to me it sounds like other options to keep the humidity and temps up might be better.

I have desert conditions in my office window and spritz everything using a facial toner bottle (a finer mist than your average spray bottle). Another modification may be a dome of sorts, but with a big gap underneath - I do this at home. Another option - to give it a shower once a week (without drenching the potting mix too - unless it needs watering).

I know, this os old, but then almost all the posts here are.

B partita does fine in terrariums, for me. The light is a big factor though, it will grow long thin stems instead of the short thick trunks it's known for in anything less than full bright light when kept that humid.

If you want to test one out, just clip the top or an odd branch and set it in the terrarium, they root very easily in high humidity.