So, does the Bible actually bear out this teaching of a pre-tribulational Rapture? Yes, resoundingly, yes!
Let me offer you an annotated list of scriptural citations which support the concept:
1) Revelation 7: note that the 144,000 are described in earthly terms, whereas the Gentile saints are described in heavenly ones;
2) Matthew 24:32-51: note that despite referencing the signs of the end, Jesus teaches the sudden, unexpected taking away of those that were ready;
3) Luke 21:36: note that the "escape out from all these things" is associated with standing before the Son of man;
4) 2 Thessalonians 2:1-5: note that the Thessalonians had thought they missed it all, not only the gathering of the saints to Christ, but the coming of our Lord. The reference only makes sense if they were expecting a "secret rapture." Paul reassures them by reiterating that the coming will not be secret, even though the gathering is;
5) Revelation 3:7-13: note that there is a Jewish/Gentile divergence referenced and that the church in Philadelphia was promised to be kept out from the hour (a short period) of trial coming upon the whole earth;
6) Luke 17:26-36: Note that the rescue in the ark was followed by wrath on the earth, which makes perfect sense in light of 1 Thessalonians 5:9;
7) Revelation 12:1-6: this will actually take some words to develop, so please read on.Perhaps no chapter of scripture is more helpful eschatologically than Revelation 12. Once one properly understands the symbols, the end-time scenario clarifies and the timing of end-time events settles into place. The imagery of the woman clearly hearkens back to Joseph's dream, the figure is obviously Jewish. That she was pregnant brings into focus two thoughts:
1) She would give birth to something like her, and
2) While in the womb that something was expected but hidden. If one sees the woman as a corporate symbol (like the nation of Israel), rather than an individual (like Mary), then the infant must taken the same way.
Interpreting Revelation 12
The woman is the messianic Jewish community, the baby in her womb is the Gentile church. The church is in the womb because it was hidden from sight from the former prophets, secreted in between Daniel's 69th and 70th week (despite the Jews being prophesied as having an effect on all nations). Though hidden, it grows and develops until it has attained its full gestation (Romans 11:25, full number), at which point, its time in utero is complete and the baby is born.
Immediately, the child is raptured (Koine: harpazo) into the heavenlies. We should recall at this point that the church is the body of Christ and that we will rule and reign with him. The Jewish mother is left, protected on earth for three and a half years. That equates symbolically quite well with the description of the 144,000. Her other offspring, who become subject to the animosity of the dragon, are the Jews who will be coming to Christ as a result of the testimony of 144,000 and the two witnesses (but that's for another article).
So, the Bible does teach a sudden and escaping translation of the Gentile church to heaven at the close of the Age of the Gentiles and the beginning of the 70th Week of Daniel. Though often pejoratively referred to as the Secret Rapture, all I can say is that the secret's out!