Yes, the Bible does say that Peter has the authority to bind and loose. This refers to the Apostolic power to forgive sins on behalf of Christ. All priests have this in the Sacrament of Confession.
But Mary is higher than that – she is not dominated by sin. From the moment she was conceived, she was immaculate, never sinning.
Peter didn’t have the same privilege. Indeed, Peter sinned time and again in the Gospels, even denying Jesus while He was in His final hours.
Saint Peter was our first Pope. Popes have been devoted to Mary, but Mary does not need to devote herself to any Pope. She is the mistress of all popes, all of mankind, all of heaven. We even see this in how the Church forms – there are numerous Catholic Orders devoted to Mary, but I can only think of one that is devoted to Saint Peter (the FSSP fraternity).
As the Litany of the Rosary says,
Mary – the Queen of Apostles.
Saint Peter, by the way, is called the Prince of the Apostles.
Nothing that was created – not any one, not any thing, not anything in heaven or earth, not even the whole heaven and earth combined – could be considered greater than Mary. Even angels have sinned, or so Saint Faustina tells us.
… Peter binds and looses on Earth, is bound and loosed in heaven? So does that mean that he can intercede on our behalf just as much, if not more than Mary?