The bridge was intended to allow people to cross __________ to the other side of the river and get to work.

When crossing a bridge to reach the other side of a river, the appropriate preposition is 'over'. 'Cross over to the other side' is a common idiomatic English construction emphasising movement from one side to the other across an obstacle. While 'across' is possible, the phrasal pattern 'cross over to' is standard usage for bridges spanning a river. 'On' and 'down' do not fit the directional sense required. Therefore, 'over' is the most appropriate preposition.