Depending on your phone and computer, you might be able to use USB or Bluetooth to connect the phone and use Android file transfer to get an iReal Pro backup copied over, or save it in Google Drive and access it from the computer.
Set up a shared folder in Bluestacks and put the backup in there so the Android environment can find it.
(Or as Bob said, email it to your email account you have set up within Bluestacks.)
Perhaps save (move or copy) it in your Android Documents folder so it can stay there as a previous backup.

You should be able to use an Android file manager app to locate the backup then open in iReal Pro.

I have not checked this works in Bluestacks, but it works in AMIDuOS.
ADMIN EDIT: has been discontinued