The bridge itself is very straightforward. There's a man you'll run into on the bridge who will offer to sell you Fresh Water for $300 — not particularly a good deal. If you decline, he'll try even harder to sell it to you, which can be rather amusing.
As the bridge starts to spiral over on the other side, there's a thirsty man who is in need of some Fresh Water. How convenient! If you give him some, he'll dash off to the Driftveil Drawbridge. If you give him Fresh Water there, then at the Tubeline Bridge, then at the Village Bridge, then the Marvelous Bridge, then the Marine Tube, he'll give you a dozen Moomoo Milk when you talk to him on the Skyarrow Bridge after doing all of that.
Keep following the bridge until you reach the gate leading into Pinwheel Forest.