No real idea, but bridges are a product of being classical roads or better.
My hypothesis is that since you do not own the other tile across the river, it might be that the western road tile (unclaimed) was created in the ancient era and still is an ancient era road, while the eastern road tile (claimed in your territory) has been updated to a classical road (or better) as you have progressed in tech past the ancient era.
Claiming the western tile should likely fix it.
Do test it though, I'm curious if my hypothesis holds true.