I went deep into the symbolism that these words have for me, for today's song. Don't know whether that will be evident in the performance.
What's a bridge? Something that goes over something that is between where you are now and someplace else.
A river is going that-a-way, its water flowing over its bed fluidly, carrying with it anything taken up by its currents.
The "I" narrator of this song is going cross-wise to the flow of the river; wherever they are, and wherever they're going, the river's path is otherwise, and it therefore (in this case) forms an obstacle. But no worries—there's a bridge, a way over, a way past.
And for a moment, a hovering-over, as the arch of one path encounters the flow of another.