Mary actually did not "reintroduce" burning as a punishment for heresy.

Burning at the stake had become the default late^1 medieval punishment for heresy, although other forms of execution were certainly practiced (and would continue to be in the Reformation era--women in particular were often drowned, but there are even a couple cases of the heretic being buried alive in the HRE). On one level, burning was a shameful and painful death (although, again, sometimes mitigation was offered, such as placing gunpowder around the base of the pyre so it would explode and kill the person right away, or having the assistant secretly strangle the prisoner while setting up the fire). More important for heresy, however, was the lack of relics as a result. Practically, other secret heretics would not be able to collect the dead body. Theologically, destruction of the physical body was thought to eliminate any chance the heretic would participate in the eventual resurrection of the body. It was a highly symbolic death in the Middle Ages.

And remained one in the Reformation. The first Protestant martyrs were executed for heresy in Brussels in July 1523, and yes, they were burned at the stake. That was the go-to method for killing heretics. Balthasar Hubmaier's (Anabaptist) wife was drowned, but he was still burned.

Under Henry VIII in England, we hear mostly about hangings and beheadings, it's true. But with exactly one exception (John Forest in 1538), the Catholic martyrs under Henry died as traitors, not heretics. They received the traitor's mode of death.

Mary's political situation was different. Her attempt to slide England back towards Catholicism after Edward had a lot less to do with her personal authority as the head of the Church of England, which was basically what the jibs and jabs at Reformation under Henry had amounted to, in the end. Under Mary, Protestants died as heretics, not traitors. Hence, burning was the default punishment--as it remained on the continent all along.

^1 Added here for clarification--see discussion below.

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Sources: Brad Gregory, Salvation at Stake: Christian Martyrdom in Early Modern Europe discusses the English situation in its Reformation context as well as the English one. Christopher Haigh, England's Reformations: Religion, Politics and Society under the Tudors explores the differences between the English Reformations under Henry, Edward, Mary and Elizabeth. If you're interested in some primary source, Anne Askew's account of her interrogation and an onlooker's record of her execution, picked up in Foxe's Acts and Monuments/Book of Martyrs, is great reading.