You might want to have a look at the multicolor bitsy version. https://aurysystem.itch.io/multicolorbisty
Viewing post in 3 colors per tile
Yes, Bitsy Color does support transparent backgrounds. You may need to refresh the page before it actually works.
You may also be interested in simply using multiple (4+) colors on your item, instead of overlapping an item tile and a sprite tile in order to get multiple colors. That is taught here: https://itch.io/t/3442509/tutorial-adding-and-using-more-colors