1.) Coconut Mulch is your new best frined. Great, great, great for humidity. Organic, doesn't mold, absorbs odors.

2.) Upgrade to a larger water bowl

3.) Wet or heavily mist the mulch, place a large water bowl inside

4.) Make sure you have an accurate hygrometer.

I use a glass cage, not a tub, so a damp cloth over the top may not work.
The humidity should be better in plastic than glass. Others will chime in - people who use tubs. But Coco Mulch is wonderful for keeping humidity stable.

Good Luck!