Fully off road isn’t that easy without being massively contrived. Off the top of my head I’d say head for Wooler then skirt Cheviots would give best off road to tarmac % and keep to decent (quiet) back roads where you do have to use them.
One way would be to head S from the end of the causeway, pick up tracks through Kyloe Woods, and then some minor roads to Wooler (basically St Cuthbert’s Way). Head W out of town through the forestry then BW over Wooler Common to Broadstruther, S to langleeford. Steep up and over towards Threestoneburn FC plantation, then SW to Linhope. Quite a few BW options in all directions here. Direct option would be cross the Breamish head S on BW to Alnham. Then either East on minor roads and then into Thrunton Woods and South to Rothbury, or South towards Thropton on byways and minor roads then pootle through the woods and down into town to finish. Not sure of the distance but a reasonably stiff day even if there aren’t many big climbs.
[edit – basically what geda said then…]