Yes, then maybe I am not understanding.
* You can make a BMP, PNG, or JPEG have a transparency pixel, that works for all formats.
* You can remove the transparency pixel when you load, or using a shader and do it every frame. If the former and you go to save a background or sprite, the image will be saved with the transparency removed.
* Bitmaps can be 8 (monochrome), 16, 24, and 32 bits