It's hard to tell from the photo how critical situation it is. The plant might survive. It needs more light and fresh air. Glass is very bad - it restricts air flow and if the plant is not completely dry, it might start rotting. I mist my plants properly twice per week over winter and I use small USB fan to make them dry faster. There is no need to soak them for 30 minutes, few seconds is enough. To support the plant try to make some kind of improvised holder from rubber coated wire with bigger diameter.

Thanks, raxidor, for your reply.

I decided to experiment. I pulled off the leaves* with black spots. None of the other leaves*, more interior, seem to have black spots. When I pulled the leaves* off I could see the bulb*, it was white and plump looking- I hope that's normal.

*=not sure if that is the correct terminology for air plants.

If the plant center is firm, it should be ok. I think the plant will appreciate some sunlight on a windowsill and fertilizer once per 2-3 weeks (can be "full" fertilizer or specialized for bromeliads and orchids). Use concentration 10-20 times lower than is recommended for other plants.