What substrate are you using?
A second small bowl could help. So could some reptile moss or even a container with something like Reptile Prime/Coconut Husks, assuming you are using paper towels.
Frankly, if your cage is open on top, not sure how much a bowl would help. The humidity will just escape!
How soon until you get an AP, or Boaphile, etc. tank? That will solve all your problems, LOL.
I keep a small tupperware type container with a lid and a small cutout with moist paper towels in it for my leopard geckos when they shed. I keep it there always, but they use when in shed. They like it dry though. I imagine it would work if you could keep humidity about 50%+ for your BCI boy, but it would need to be big enough for him to get into. Space requirements again.
There is another option, assuming cost isn't a big deal, and it will take while to get a proper enclosure. Boaphile is 5-6 weeks, and I am not sure about AP.
There are other semi-enclosed options. Where you could use what you already have in terms of heating, except maybe the UTH.
http://reptile-enclosure.com/Front-Opening-with-Doors
http://reptile-enclosure.com/Front-O...ing-with-Doors
I have their 40G I used for my BCI before I got my Boaphile tank setup. I am not saying you have to do business with them, but something similar maybe? They are in CT, where I live, and picked up from them directly.
Way better than glass, but you have to supply all the heating elements etc.
Any reptile shows near you? Maybe you can get something better in the meantime? Just trying to think outside the box.
I think glass works if your room is okay to begin with. Your room sounds like a disaster for a BCI and you are working really hard just to maintain.
I'd be thinking of another enclosure ASAP, or a better room/house! I am guessing the enclosure is the best way to go.
I rambled here, but I am trying to give you all the options.