The epithet "Bloody Mary" is associated with a number of historical (particularly Queen Mary I of England) and fictional women, especially from folklore. It is believed that inspiration for the cocktail was the Hollywood star Mary Pickford who earlier had a similar cocktail consisting of rum, Grenadine and Maraschino named after her.
In 1934, the cocktail was called "Red Snapper" at the St. Regis Hotel, where Petriot was hired at the time. It was here that Tabasco sauce was added to the drink, and the name "Bloody Mary" eventually won popularity. In the 1960s it became popular to serve the cocktail with celery due to a guest at The Pump Room at the Ambassador East Hotel in Chicago.
The name likely refers to the blood-like color of the cocktail.
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The person is Mary I of England
Check out Wikipedia for more on her.
http://en.wikipedia.org/wiki/Mary_I_of_England