All PVA glues (permanent white glues) will soften if exposed to water more than a short while (and will also turn cloudy since they absorb water just a bit). After they soften long enough, they will usually release from the surfaces they've been attached to, especially if those surfaces are *smooth*.
Glass is quite smooth so it's not easy to "glue" things to it under water, although if there won't be much disturbance to those areas there probably won't be a problem with the non-softening glues.
Other glues you could try would be:
...epoxy glues (or epoxy resin)
..."Gorilla Glue" though that must be weighted or clamped while setting because it swells
...Liquid Nails?
...instant glues (those won't work as well on porous items, and must have total contact as much as possible, but could work especially for the rocks--and the rocks could be set in or around the moss so that it held that down with a *mechanical hold* as well as an adhesive hold)
... E6000 type glue
... perhaps hot glue
Re epoxy resin, you could also pour it into your bowl, then place the rocks and moss** into the resin, then let cure (or let the resin sit till it gels, place the items on top of that layer, then add more resin, and let cure).
Then fill the rest of the bowl with water (the separation line between water and resin should disappear visually).
The best kind of resin to use for this might be "floral setting resin" (buy it in the artificial flower dept at Michaels, at Walmart, or at floral shops, etc--brands like Quick Water, Aqua Illusion, etc):
https://www.google.com/images?q="floral+setting+resin"
Or perhaps use a tweaked epoxy resin brand like Easy Cast, which is similar but will cure really hard.
Check out my previous answers here for more on resins, Easy Cast, etc:
https://answersrip.com/question/index?qid=20091115185640AAXBfZF
Easy Cast info/instructions, many of which apply to other epoxy resins:
http://www.sculpt.com/technotes/Tech_Sheets/TECH_SHEET_EasyCast.pdf
**dip the moss into the resin first so it can get in and around all the spaces between the strands/etc which will help prevent bubbles later, etc