The 8 bit BMP uses a color table, which has 256 entries (one for each byte value) 4 bytes each (3 for RGB and 1 for alpha or just for alignment). (But: read the comment by user763305.)
Anyway, have a look at the PNG format, it is usually the easiest format for lossless image file interchange. You can choose between 1-bit grayscale (i.e., B&W) and 8-bit grayscale.