The US has no armed drones that can operate at such high altitudes, and the UCAVs that do exist don't carry machine guns that could be employed against airborne targets. In theory it would be possible to design or modify such a drone but that would take a while.
Using guns against high-altitude balloons is also challenging just from an aerodynamics standpoint. Stall speeds get pretty high up around FL600 even with large wings, so the airplane would have to fly straight at the target with a high closure rate in order to get within effective gun range. This creates some risk of a mid-air collision. Using a guided missile is much safer.
Problem with shooting them down is that you need a lot of bullets to get the thing to plummet. Helium is always leaking a bit anyway across the entire surface, so adding a few hundred small holes doesn't accomplish as much as one would hope.
In WWI the UK developed AA rounds to shoot down zeppelins and balloons. They were basically tracer rounds with a bigger incendiary charge that ignited when fired and set the skin and hydrogen of balloons on fire.
Modern incendiary and explosive rounds fired by fighter jets aren't effective against them becayse they are only triggered by their impact against a hard target, but I'm sure the DoD could come up with a more effective version pretty quickly if it came down to that.
At their size, the balloon would slowly descend (into public airspace) when shot at with even high calibre jet mounted guns, if i understood correctly.
Can't balloons be punctured by something less expensive than a stinger? Maybe a drone with a machine gun?
And that leads to the conspiracy that there's someone already has a balloon defense system ready for the inevitable bid.