CoastalMaya Don't worry about the second files (starting with "._"), on maOS these are normally hidden system files (but not on other platforms), and can be ignored.
Could you elaborate on the .bmp file which couldn't be transferred? I was assuming you copy the three files (.exp, .inf and .bmp) manually on a USB stick… This file should be used to display a preview without reading / interpreting the whole design. From your description I take it was not used by your Bernina 570QE although it was present on the stick?
Edit: I just modified my answer for more clarity, and I sincerely apologize I forgot a big "Thank you, Maya!" 🙂