Of course all those doctrines are biblical.
Do you accept the doctrine of the Trinity? It's not literally in the bible but the concept IS....
Do you accept the hypostatic union, the fact that Jesus has a divine nature and a human nature but only one divine person? That's not spelled out directly in the Bible, but the concept can be understood by reflecting on the clues in the bible.
What so many fallen away Catholics and most Protestants utterly fail to understand is basis exegesis. They fail at basic, 101 level interpretation.
For example, many will be proof texted about "call no man Father" - utterly oblivious to the fact that in the same Gospel, Matthew begins by calling plenty of men "fathers" and Jesus himself, when reciting the ten commandments reminds people to honor their fathers..... thus, if that line is to be a LITERAL condemnation, both Jesus and the very same Gospel writer himself violated the so-called "literal" interpretation!
With respect to purgatory, Marian devotions etc. the problem is too LITTLE meditation on the Bible not too much. People read their bibles in little bites rather than whole chapters or whole books all at once and seem to forget how the Old and New are to work together and how the New works together as well. You can't read Hebrews while forgetting about the Gospel of John or Acts. You can't read the letter to the Romans while ignoring the Gospel of Luke. It's all got to fit and balance.
Thus doctrines like Purgatory draw on Maccabees and the book of Revelation for inspiration as to some state of further purification after death but before entering the glory of heaven. The souls therein are already 'saved' so it's not like they were otherwise damned. No, they had faith, they had love but it was as yet unperfected love. How long this state of purification lasts is impossible for say because without a resurrected body it's impossible to know how time works.
But typically the logic goes :a) Church must be wrong b) I don't understand this doctrine therefore c) doctrine must be un-biblical and d) I will stubbornly refuse to read the scripture as the early Church fathers did who came to conclude that this must be how things are.
It's silly.