It wasn't actually fired by John Wilkes Booth, he just happened to stand there with a gun in his hand ... the bullet is a perpetual device that has killed countless world leaders all the way back to Jesus Christ who was killed on the cross by the bullet.
And like you say, the bullet continues to move through time and it will strike again
The authorities quickly framed Oswald to prevent outbreaks of mass panic at the inexplicable death of the nation’s highest official.
Can you imagine what would happen to the Dow Jones once everyone realised that anyone’s head could spontaneously explode at any time, even if they’re the President, riding in a motorcade in front of hundreds of spectators and full police security?
After Dallas 1963, the Secret Service must have lists of potential patsies in every location, to frame if anything like this would ever happen, just in case. That NSA supercomputer in Utah? That’s not just for decrypting everyone’s IMs, it’s also for synthesising realistic backdated CCTV footage of the next Oswald taking his shot, in case the unthinkable happens again.
It traveled through time at the speed of regular time, then dipped outside of spacetime for 18 years before reappearing inside Kennedy's skull.