Personally I'd reinstate it as a straight line as on the Bedford Council map but I don't think most folk would worry about it.

I've just reverted your next changeset as they are two separate paths. The short piece to north is the truncated section of the Bedford FP 1 footpath. Bedford FP 1 carrys on down Brookfield Road where it's tagged as highway=residential, designation=public_footpath and foot=designated.

Please don't be put off mappin by this, there's a lot to learn in OSM.

Regards Bernard.