The bridge over River North Esk is in a very bad shape. The sign states: "Do not cross (the bridge). Do so at your own risk." That is what we did and made it. Nonetheless, I would not recommend it. Even if you make it from the shore coming out of Tarfside all the way over the bridge, it is very challenging to get over/around the barbed-wired steel fence on the other side of the bridge. Especially if you carry a heavy backpack. You might rather consider just fording the river if the water level is low.
There are also fairly good spots to ford the river a little further down. Just look at your map to find a road that seems to cross the river.