The question is a bit tricky, because it depends on what you mean by "shuttle".

* Space Shuttle: The Space Shuttles were designed for low Earth orbit and never went to the Moon.

* Lunar Module: The Lunar Module was part of the Apollo program, designed specifically for landing on the Moon. It took about 3 days for the Apollo missions to reach the Moon from Earth.

So, while there was no shuttle that went to the Moon, the Lunar Module, a spacecraft specifically for lunar missions, took around 3 days to reach the Moon.