How can Mary be the mediator between God and men, if the Bible says there is ONE mediator?

You're exactly right. Some churches have deified Mary, but that should not be. She was just a godly woman who was chosen to give birth to Jesus; she's not a god/goddess or the mediator between God and men. As you've pointed out, the Bible makes it clear that Jesus is the only mediator between God and men. Or else, Jesus wouldn't have said in John 14:6 - "No one comes to the Father except through me."