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The earliest extant reference to John being thrown in boiling oil from Tertullian, c. 200. His casual mention of the event suggests that it was a widely known story during his day, although it is hard to say by what amount of time the story predates Tertullian.
If the story has any basis in fact, it is usually assumed to have taken place late in the reign of Domitian (81-96). The only book of the New Testament that directly covers church history, The Acts of the Apostles, ends in about 61. Assuming Johannine authorship of I John, II John, and III John, all three would predate the boiling incident. The remaining Johannine literature - Gospel of John and Revelation - would not be expected to mention it either. Thus, we would not expect the story to be mentioned in the Bible, even if it is true.