The pedestrian generally has the right of way, but because of the bicycle's momentum and the difficulty of swerving the bicycle to avoid a collision, it might be a very good idea for the pedestrian to be polite and move aside.
In Massachusetts years ago we discovered that a governmental "trails committee" wanted to put in regulations that would establish separate trails for the various uses. Some for bicycles, some for hikers, some for four-wheeler enthusiasts, some for horses, and a very few for motorcycles. Very little mixed usage.
We got together with the various trail users and pointed out that this was "divide and conquer" and that nobody would be allowed on most of the trails. Our own experiences as horsemen convinced us that sharing trails with those other people was easy, friendly, and fun. Indeed, we sometimes took our horses out to help do construction work in places that had become inaccessible because of washouts. -- Can't get a tractor in there, but one horse with a proper harness (or even a Western saddle) and a strong rope can pull that culvert back into position!
Work with other trail users. Become their friends. And try to educate the ones who want to ban certain kinds of people and vehicles.