As much as you want...
Bubble gum can't do what your character is able to do with it, so the natural properties of gum don't apply. However, I'm assuming you'd like the gum to behave somewhat, well, GUMMY, so here's what I think.
If your character can manipulate gum infinitely, they can store up pressurized gas inside the bubble (how to get it in, I don't know - someone suggested inflating the bubble to huge size, then shrinking the whole thing) and condense the gas to millions of kPa. Theoretically releasing this much pressure can be as devastating as you want, if the character can do it remotely (otherwise, they might vaporize themselves...) https://en.wikipedia.org/wiki/Effects_of_nuclear_explosions The gum could even be "inflated" with explosives, and the gum contain the burst, storing the force for later. This could be defensive (I imagine a time bomb going 3-2-1 DUD, but the character now has a massive explosion stored up for later).
Also consider volume of the gum and controlling adhesive properties. If you can expand the gum, or convert unchewed gum instantly to a chewed form, the gum could behave much like less-lethal foam. https://en.wikipedia.org/wiki/Sticky_foam Applying the same gum to someone's respiratory tract could cut off breathing and kill someone. If the gum is made to behave in an amoeboid fashion, but an edge is created that is hard and razor sharp, the person could have a sort of remote assassin, especially in a gum-rich environment like a subway or public school. It could slice someone open, crawl in and then plug the arteries going to their heart or brain. No one would understand what happened until the autopsy.
You can give such an ability as much or as little power as your creativity chooses. Kind of a weirdly specific ability, but if it is so limited to range as only gum, make every stick count.