When Bill O'Reilly talks about Hell, salvation and what he thinks “the Catholic Church” teaches about “baptism of desire,” keep the following facts in mind:
It’s a solemnly defined dogma of the Catholic Church that all who die as non-Catholics go to Hell. This was defined by popes ex cathedra more than seven times, including by the Councils of Lateran IV, Vienne, Florence, Lateran V, Trent and Vatican One.
It's also a dogma that faith in Jesus Christ and the Trinity is absolutely necessary for salvation for all above the age of reason. This was defined by the Council of Florence and the Athanasian Creed.
Any modern text or “catechism” that would contradict these truths is not Catholic, heretical and to be rejected.
Here's the dogmatic definition of Pope Eugene the fourth, at the Council of Florence in 1441, ex cathedra:
“The Holy Roman Church firmly believes, professes and preaches that all those who are outside the Catholic Church, not only pagans but also Jews or heretics and schismatics, cannot share in eternal life and will go into the everlasting fire which was prepared for the devil and his angels, unless they are joined to the Church before the end of their lives; that the unity of this ecclesiastical body is of such importance that only for those who abide in it do the Church’s sacraments contribute to salvation and do fasts, almsgiving and other works of piety and practices of the Christian militia produce eternal rewards; and that nobody can be saved, no matter how much he has given away in alms and even if he has shed blood in the name of Christ, unless he has persevered in the bosom and unity of the Catholic Church. End quote.