Yes, bi-colors and calicos must have one parent that is a bi-color or calico.  The gene responsible for this (the white spotting gene) is a dominant one so it only takes one bi-color parent in order to get bi-color kittens.  The amount of white generally increases when you breed two bi-colors together as opposed to breeding a bi-color to a solid.

I assuming by high white you mean the van pattern?  Bi-color to bi-color breedings give you 50% bi-color, 25% van and 25% solid, statistically speaking of course.  Bi-color to solid breedings give you 50% bi-colors and 50% solids.  Van to bi-color is 50% van and 50% bi-color while van to van is 100% van.  A van bred to a solid will produce 100% bi-colors.

Yes, I also love those pics of Lady!  What a beautiful girl she is!!!