The victory sets up a Quarter Final match up away to Enfield 1893. Date and kick off time to be confirmed.
The match was won in the first half after goals from Justin Amaluzor, Nana Kyei and Fumnaya Shomtun gave the Bees a comfortable lead at the break.
Ashford bagged a consolation goal in second half stoppage time, courtesy of an Alex Fisher spot kick.
A short highlights package will be available shortly.