Couldn't find a better video than this one example. (You can see it at the start, at 14:56 or at 15:46)
(Video taken from Huahwi, pls no hate<3)
It would be really hard to get someone when walking off a bridge because first, you're moving so they have to guess where their rod is going to land, second, they most likely have a long distance from themselves and the bridge, and third, if they caught you and you keep running before they retrieve the rod, the line would break cause of the distance.
Just to add to this post that has nothing to do with was I just said^... Another strategy of using it would be for example when you're on a bridge trying to go on someone's island but you don't jump or go there because you fear to get hit off, if you use the Fishing Rod and pull that person, you could get the kill, and even if you don't pull them off their island, then your opponent would most likely go to a safer spot than being on the front line to death :p