Would firing a gun at the right angle on the moon put the bullet in orbit

Or would the bullet have escape velocity from the moon? and either:
Crash into the earth,
Orbit the earth,
Crash into the sun,
Orbit the sun
Or would it not be able to escape and simply fall back to the moon after some not overly long period of time.

If the bullet were fired at the correct speed it would orbit. Lunar escape velocity is 2,380 meters per second and orbital velocity is about 1,680 meters per second.

Gun muzzle velocities range from approximately 120 m/s to 370 in black powder muskets, to more than 1,200 m/s in modern rifles with high-performance cartridges such as the .220 Swift and .204 Ruger. That is still too slow for orbiting the Moon.
Tank guns firing kinetic energy penetrator ammunition can be as fast as 1,700 m/s. That would be fast enough for orbiting the Moon.

No gun could reach escape velocity.

no hand held or portable "guns" can achieve escape velocity from the moon.... some of these big "cannon" looking things on battleships are actually properly called guns, so yes, you could achieve escape velocity with a "gun" from the moon.... hitting the earth with a ballistic shot, even WITHOUT an atmosphere on the moons surface would be nearly impossible. Orbit? never in a million years.

If you could fire a bullet that had enough speed, (I think lunar escape velocity is about 5500 mph, so about a mile a second or so - and you could send the bullet out and away, into solar orbit, or towards a trajectory toward the Earth.

it wont go in orbit much as gravity will pull it towards the earth, the bullet has very little mass..therefore it cant escape gravity

Uh...a firearm cartridge needs oxygen for detonation.