A small arms round costs cents at scale. A big balloon like that costs hundreds of dollars, and the drone hundreds more. The bigger question is if a bullet would do enough damage.
For targeting the balloon, the eventual best weapon might just be a sickle-ish blade, either on a rod or rope. Melee weapons worked for most of human history, and if your target has airspeed zero, why not? If you're hitting the drone, you'll need something more heavy-duty; small arms, a small mine or a powered blade. I suppose just tangling it or lassoing on a drogue chute could work.
The obvious choice for interceptor drone is a small blimp. It's faster then an unpowered balloon, but still very stable and capable of extreme altitudes.