Bloody Mary is actually quite a simple song, it's not that deep. It is sung from Mary Magdalene's point of view.
Lady Gaga herself said, "Bloody Mary is quite subtle actually, it's a song about Mary being divine and human at the same time, with a subtext (maybe it's not even a subtext) about the role of a woman who is supposed to be a superstar and a real woman at the same time. Not life alteringly deep perhaps but it works as a pop song."

The first verse is about how people don't understand the love Mary and Jesus had for each other, and that when he's gone she'll tell people she worshipped him. She will refuse to let Pontius kill Jesus, and will withstand any punishment (such as stoning) for this act.

Then she says she will continue to pray like he told her to, and she knows he will die so she forgives him (for leaving her) before it happens.

The chorus is her explaining that even though she feels pain, she won't show it, because she's Mary and needs to be strong, even after he's gone. Her saying, "I won't crucify the things you do" means that she won't judge or punish anything Christ does, as Pontius does.

The second verse refers to Michelangelo's statue of her and Jesus after his death, and how you cannot depict the full extent of her fury even in art form. She says she will wait for death to join him because "Je ne veux pas mourir tout seule," which means "I don't want to die alone" in French.

Then the rest is a repeat of what she says before, until te end where she says "Liberdade e Amor," which means "Freedom and Love" in Portuguese.

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