batch convert bmp to png or jpg depending on alpha?

[shadowpower]

I have a lot of .bmp in different folders, some have alpha channel and some don't.
is it possible to batch convert a bunch of bmp and detect if they have an alpha channel

if they have alpha channel convert them to .png with transparency
if they don't have alpha channel convert them to .jpg (to reduce filesize)

or is it possible to convert them all to .png and if they don't have transparency (because the .bmp didn't have an alpha channel) convert them to .jpg and delete the .png that were converted to .jpg

[xnview]

no sorry