In reply to "I mean how fast would a comet have to be going to get to the nearest star anyway?"
Comet speeds
There are relatively big varieties, but most of them is between 10 and 70 km/s. If a comet is a periodic comet, that means it needs to have an elliptic orbit around the Sun. That gives an upper limit to its speed of the escape speed from the solar system on the orbit of the Earth. That is around 40 km/s.
This is taking the fastest speed beyond which the comet would leave the Solar System.
Being near the Sun the comet would be travelling near its fastest.
At this speed I make it 4.367 / 0.133 years approx. 32.8 years to get to alpha Centauri.
I suspect my math might need rechecking, but Ihave taken fastest speeds throughout the calculation so it would be erring on the top side giving the shortest journey time.