You were going in the right direction.
To get to Maiz Prairie you have to go across Karu forest and Muyu Desert. So from the bridge you passed by go in to the forest and head to the top left of the forest, there will be an opening which leads into Muyu Desert (theres 3 openings from my memory, one closer to the middle of the forest). Once in Muyu desert you can head to the top left via Mustangs or Ostrich if you dont have a pet. The mustangs/ ostriches should take you to Maiz Prairie depending on which one you ride.
If you're still stuck or unsure of where to go you can post a screenshot of where you are. Or you can refer to this map if you have troubles seeing where to go.
File:Iria.jpg - Mabinogi World Wiki