From one side of the bridge to the other

Question

Let's say we have a bridge over a river. If we say "cross the bridge" or "go across the bridge", or "go over the bridge" we mean this movement:

But what do we say if we want to go from one side of the bridge to the other?

Answer 1

Exactly that. The 'other side' of the bridge in this case would mean across the pathway. Bridges have 'ends' and 'sides'. To refer to 'the other side' in common English is only appropriate when not on the bridge.

Answer 2

In the case of the graphic:

I crossed the roadway (in the middle) of the bridge.

If the bridge were simpler, providing only a basic surface to cross:

I moved from the right edge to the left edge of the bridge.

I cannot imagine things should be more complicated than that.