Park at the marina in Bangor, and you have options either east or west along the coast.
Great information about North Down Coastal Path, including detailed maps, on WalkNI.
NOTE: The trails on this site have been ridden before, but you should not interpret their inclusion as an indication that mountain-biking is officially sanctioned on them. Seeking permission from landowners is your own responsibility, as is conducting yourself in a manner that is courteous, respectful to the environment, and conscious of the safety of others.