If you’re just worried about your target point, probably. But you could also hit any other point about equally easily.
If you want your bullet to travel along that plumb line, no, that’s impossible, unless your bullet has precisely-controlled onboard rockets.
As I understand it, geo-stationary orbits are in the 23,000 mile range…or am I missing something?
You have low earth orbits below 160 km but you have to maintain a speed of around 8 km/sec in order not to lose altitude. I doubt if GS orbit at that alt is possible right now.
Geostationary orbit–at which a satellite is orbiting at the same speed as the Earth below it is rotating–is only possible at 35,786 km (19,323 nmi or 22,236 statute miles) and at 0° inclination. There are a wide family of geosynchronous orbits, but they’re all well above Low Earth Orbit where you have to go very fast in order to continue to fall above the horizon. The only way to travel at a geostationary speed in lower orbit is by constantly thrusting against Eart gravity.
Stranger
So back to aiming at a target which was never specified on earth… so I was always thinking target was moon based.
My question is then: Would it be possible to shoot your own self in the ass on the Moon? 
Yes, it would be possible, if you had a sufficiently fast gun. The needed muzzle velocity is higher than that of real-world guns, but it’s not so much higher that it’s completely implausible.
It’d probably also help to stand on top of a high mountain when you do it.
It didn’t take all of Mike’s processing power to work out trajectories; he programmed his “idiot son” computer to do that if need be. The complex part in-story was doing multiple simultaneous targets in real time. (Although, frankly, I think Heinlein overestimated the computational complexity of this task.)