re: Best grass to have in a shaded area

The problem is you probably won't find anything that will provide some consistency with the bermuda. Anything that is shade tolerant will likely look much different.

If it wasn't a bermuda yard, tttf would be a good grass as it has a nice color and relatively thin blade. It would be a stark contrast from bermuda, though.

Rye also works well in shaded areas that hold moisture but again, it would look drastically different.