Hard to say really. I'm sure some glues are non-toxic but if you apply heat to them that may change. I recently saw a TV ad for a sort of super glue that hardens when a certain UV light is shined on it...but again, heat may make it emit toxic fumes.... Try google....
To be clear it wouldn't be used near the bowl would the heat from the smoke be enough to to do anything?
hot glue gun works well enough if as long as you keep heat / direct flame away from it. high temp epoxy is another good fix that i have used many times myself. you can get it from any automotive parts store. just be sure it is high temp / high heat. that should get you started. what exactly are you looking to do exactly?
The beaker on my bong broke (shattered) but the entire tube from mouth piece to the top of where the beaker was is fine so I bought a new beaker and want to connect them I Will post pics tomorrow
If I were you I would avoid any type of glue whatsoever anywhere near the bowl of your piece, or anywhere on it for that matter. If it's homemade, a hot glue gun is fine but not near the bowl piece.
honestly just go get a jar or vase that thing will fit into then fill the bottom of said monstrosity with epoxy till the two glass pieces merge. Let it dry then get hella high. Use glass beads for filler / as needed.