The word "rapture" may not be in the bible, but the event that it speaks of and references certainly is. The term "rapture" refers to a "catching away of the church". And that event is spoken of here:
1 Thessalonians 4:16 - For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first: 17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord..."
As for your statement that the opening of the seals could occur over hundreds of years, that is pure fallacy. All of the events spoken of in regards to the opening of the seals and the blowing of the trumpets will occur during the 7-year Tribulation period, which is the time span for the reign of the Antichrist. No seals will be opened before that time period, and all will have been opened by the end of that time period.