This is going to be a relatively short answer, so I apologise if it does not meet the usual standards. However:

There was no such annulment.

Although a potential divorce was discussed as a means of restoring Mary's position, this never came to fruition, because it would have brought Mary even further into disgrace and dishonour. Although both lived apart in the later years of their marriage due to imprisonment and exile, they remained married until Bothwell's death in 1578.

Goodare, Julian. "Mary [Mary Stewart] (1542–1587), queen of Scots." Oxford Dictionary of National Biography. 23 Sep. 2004