Seraphin84: Sorry, there is no way to get a bridge without having land on the other side.
If it must be a bridge, you would need to fill as much land on the border, as you need to build a bridge in the regular way. But such a small island wouldn't fit to your original situation too.
*edit* After having a closer look on the photo, it may fit as the river is quite smaller at the bridge than at the other parts of the river */edit* An absolute individual modding solution would be a ferry port designed as eye-candy bridge for both sides of the river. I don't think there is something like that yet, but you may search for something like that anyways.
I think, the best solution would be a map where both sides of the river would be on the same map tile, but the river as whole placed just next to the border of one map tile.
I'll figure something out. :P Thanks for lending an ear, I could talk about this stuff all day.