I'm sure there's an Win8.1 ISO out there. I'm also sure it's an illegal bootleg and no one can be posting links or anything for it here (since it would probably be the full Win and not just the update patch--why not look on MS' website to see if you can download 8.1 separately).
As to your bluetooth mouse issue--do you have any other bluetooth devices that work/don't work, and you may have an external interference problem unrelated to the Surface itself.
Update: Make your own ISO legally.