You can approximate your bipartite graph visualization in NodeXL, and even improve on it by removing edge crossings. I took your sample bipartite graph, and in the image below I colored the nodes by their side (u or v). They are laid out using the Sugiyama algorithm that minimizes edge crossings. I did this in the interactive NodeXL template for Excel 2007--2013, but all these features should be available as the standalone NodeXL C# and WPF class libraries. The current libraries as of this post are available to download here.
I also tried NodeXL's group-in-a-box layout to separate the groups and display them each individually in a grid, with marginal results.
Disclaimer: I'm an advisor for the NodeXL project.