Catholic.com has some wonderful resources regarding all sorts of catholic topics, including Purgatory. I found this which gives you some biblical support to the concept. While the word “purgatory” may not be in the Bible, the concept certainly is.
"Christ refers to the sinner who “will not be forgiven, either in this age or in the age to come” (Matt. 12:32), suggesting that one can be freed after death of the consequences of one’s sins. Similarly, Paul tells us that, when we are judged, each man’s work will be tried. And what happens if a righteous man’s work fails the test? “He will suffer loss, though he himself will be saved, but only as through fire” (1 Cor 3:15). Now this loss, this penalty, can’t refer to consignment to hell, since no one is saved there; and heaven can’t be meant, since there is no suffering (“fire”) there. The Catholic doctrine of purgatory alone explains this passage.
Then, of course, there is the Bible’s approval of prayers for the dead: “In doing this he acted in a very excellent and noble way, inasmuch as he had the resurrection of the dead in view; for if he were not expecting the dead to rise again, it would have been useless and foolish to pray for them in death. But if he did this with a view to the splendid reward that awaits those who had gone to rest in godliness, it was a holy and pious thought. Thus he made atonement for the dead that they might be freed from this sin” (2 Macc. 12:43–45). Prayers are not needed by those in heaven, and no one can help those in hell. That means some people must be in a third condition, at least temporarily. This verse so clearly illustrates the existence of purgatory that, at the time of the Reformation, Protestants had to cut the books of the Maccabees out of their Bibles in order to avoid accepting the doctrine.
Prayers for the dead and the consequent doctrine of purgatory have been part of the true religion since before the time of Christ. Not only can we show it was practiced by the Jews of the time of the Maccabees, but it has even been retained by Orthodox Jews today, who recite a prayer known as the Mourner’s Kaddish for eleven months after the death of a loved one so that the loved one may be purified. It was not the Catholic Church that added the doctrine of purgatory. Rather, any change in the original teaching has taken place in the Protestant churches, which rejected a doctrine that had always been believed by Jews and Christians."