There's no right
way to do it. There are common ways people work (using png spritesheet), and using bmp, for me, is like a suicide. It's huge in size, and it gives you nothing more. So if you're asking if this is the 'right way to do it' - no. It's up to you to decide.
Having specific background is commonly used when using the blitting technique, which basically updates the BitmapData of one Bitmap object which is on stage. Copying pixels is somehow fast in flash, so you can achieve the effect of actual moving objects simply by copying pixels to specific location of the bitmap.
You can remove the background by many ways - threshold, blending, or simply copy specific pixels.
I guess BMP file doesn't need decompression, thus it's going to be processed somehow faster, but it's file size is increased. As the decompression (especially on small images) isn't that of a problem (GPU upload is slower) - the common way is to use PNG or at least JPEG.