I think there are only two ways to traverse this route--either over the Heart of America bridge, or the Fairfax bridge. The Fairfax route has the benefit of being the most direct. The northbound part of this bridge is not terrible in that there's a small shoulder one can ride in. Southbound on Fairfax (the older deck) is a bit more hair raising--no shoulder to speak of, so you should take the lane. Traffic is not heavy. Fairfax trafficway is kind of a pleasant ride in both directions.
Heart of America has more traffic, and I think you need to be on 9 hiway at some point.
Feel free to contact me directly for more specific directions. The routes are not difficult.