I had this exchange on What would have happened if the Balrog of Moria had taken possession of The One Ring? with Jeremy French.
Jeremy French: But how would he have got it to fit?
DavRob60: That would not be a problem, as the ring has been show reducing his diameter by himself to suit Isildur finger. We could safely assume it would be able to expand again to fit the Balrog's finger. As Konrad Rudolph commented here, at the beginning of LotR, Bilbo (?) mentioned that the ring became sometimes looser and sometimes tighter.
Jeremy French: the ring changed because it wanted to fit on Isildur's finger. It would not want the balrog to challenge it's master so why would it accommodate it?
So, would the One Ring scrupulously serve a powerful being like the Balrog, Saruman or even Gandalf, or would it plot to get back to its master and ultimately betray its bearer, like it did for Isildur?