I am currently implementing something quite similar to checkers. So, I have this table game and there are both white and black pieces. Where there are neither white or black
I would also use a bitmap for this. The functions to check for 1, 2, and 3 will be a little unintuitive to write, but should be very fast.
You'll, of course, need to be careful of the edge cases and a fast solution will probably involve some integer and modular arithmetic on the indexes.