Convert image to 8 bits per pixel adaptive color BMP using ImageMagick

The input image is color (not grayscale) but with very few colors (<16 colors).The output image must be 8 bits per pixel (not 4 bit per pixel/not 8bit per color/not grayscale) BMP.The converion must be lossless. (unless the colors more than 256)

What ImageMagick parameters should I use to achieve it ?

Thanks!

I have tried some parameters like:

-colors 256-type Palette or optimize-depth 8

But they all output a 4 bits per pixel BMP.I want to ensure the output image a 8 bit per pixel BMP.

Any command-line solution other than ImageMagick is welcomed.