I've heard that Queen Mary I of England have another name that is "Bloody Mary". and there also is a folklore about the Bloody Mary which is about holding a candle in front of mirror. Is there any possible link between the two stories.
Well, Bloody Mary is generally confirmed as folklore, so any connections to any historical person is shaky. Mary I of England got that sobriquet because of hers executions of Protestants and Bloody Mary probably got that name because participants may endure the apparition of drinking their blood.
However, if you look further, you could see some connections between two of them.
Wikipedia article says:
A modern addition of taunting Bloody Mary regarding her baby indicates the legendary figure's tenuous connection to Queen Mary I, also known as "Bloody Mary", whose life was marked by a number of miscarriages or false pregnancies.
When she was 38 she gained weight, stopped menstruating and felt nausea. Doctors thought that Mary was pregnant, but it was most likely a false pregnancy, perhaps induced by Mary's overwhelming desire to have a child.