First bring all villagers together , convince them the need and see that they promise to vote only the party who construct the bridge
second you have to plunge into the politics contest with/without any party affiliation in corporation/ panchayat elections of your village (with a sole promise of constructing the bridge)
You can also motivate the villagers to construct a check dam so that the water is not wasted and also the above problem is sorted out
meet the panchayat president discuss with him the need of the bridge (if need be blackmail him of votes) offer the required manual assistance by the villagers so that only a small part of the allocated money for the village is spent)
and finally make a neat visual presentation, invite/present the same the media personnel and see the impact for yourself.