Surprised not to have seen this on here already, but the
Buccleugh Arms Hotel in Moffat is a proper bike friendly pub/hotel, owned and run by a family of bikers.
As I only live half an hour down the road I can't comment on the rooms etc, but we've eaten there a few times and it's really good.
I think they've got secure bike cages round the back now for overnight storage (better double check that as I'm not 100%).