There is a way of drawing transparent sprites to the screen just using BitBlt. But it's not soft alpha transparency, it's either transparent or not.

Here's how to do it:
1. Make all the areas of the sprite that should be transparent black
2. Create the mask, making all the areas that should be transparent on the original sprite white. Make all the areas that should be blitted unchanged to the destination black (ie. make the rest black).
3. BitBlt the Mask onto the destination with the SRCAND raster constant.
4. BitBlt the original sprite with the SRCPAINT raster operator.