Short answer: No, there has been no change or corruption of the Bible.

We can verify the integrity of the Bible because of historical evidence, and even from what the Quran says. The reason for this claim is the Islamic Dilemma.

Historical evidence

The reason we can trust that the Bible text we have today has not been changed or corrupted is because we have originals of the text dating back almost 2300 years.

The Dead Sea scrolls

The Dead Sea Scrolls contain parts of all but one of the books of the Tanakh of the Hebrew Bible. The texts they contain are identical in meaning with modern Bibles. This shows that the transmission has been so faithful that nothing has been changed or lost for over 2300 years.

Complete Bibles

We also have several complete Bibles that are several centuries older than Islam. For example the Codex Sinaiticus (4th century), Codex Vaticanus (4th century), Codex Alexandrinus (5th century), and Codex Ephraemi Rescriptus (5th century). This means that they are 200-400 years older than Islam itself. These are complete or near complete Bibles from 1600 years ago and their contents is identical in meaning to the contents of modern Bibles. This proves that there has been no changes between then and now. The Bible that existed in the time of Muhammad is exactly the same as the Bible we have today.

Church Fathers

Apart from this we also have the writings of the early church fathers who wrote between ca 50 CE and 300 CE. They quoted the Bible so much that from their quotations alone we can reconstruct the entire New Testament. This proves that the New Testament we have today is exactly the same as the one they had in the second to fourth centuries.

Other sources

Apart from these, we have smaller books, or chapters of books, or even fragments going back even farther. The oldest ones date back to 250 years before common era, that is more than 2270 years. All in all we have over 10.000 Latin manuscripts, over 6000 Greek manuscripts, over 2000 Hebrew manuscripts, and thousands of manuscripts in other ancient languages. The Bible is the most well preserved ancient text that exists.

Historically speaking there is absolutely no evidence of any corruption or missing information.

The Quran affirms the Bible

Surah 2: 88-91

And when there comes to them a Book from Allah, confirming what is with them… When it is said to them, “Believe in what Allah Hath sent down, “they say, “We believe in what was sent down to us:” yet they reject all besides, even if it be Truth confirming what is with them…

The Quran confirms the Bible that “was with them”, or that they had in the 7th century saying that it was uncorrupted and coming from Allah. Since the Bible is exactly the same before Islam started as it is today, and the Quran says that the Bible that the Christians and Jews had is confirmed by Allah, how can any human disagree and say that it has been corrupted?

The Islamic dilemma

The reason for saying the Bible is corrupted is because of what is called the Islamic dilemma.

1. The Quran says that the Bible is the authentic, preserved word of Allah. (Surah 2:41,89,91,97,101;3:2,3,81;4:47,136;5:44,46-49,68;6:92;10:37,94;12:111;21:7;29:46;35:31;37:37;46:12,30)
2. The Quran says no one can change the word of Allah. (Surah 6:34,115;10:64;18:27)
3. Therefore the Quran says that the Bible has not been changed.
4. Yet the Quran also contradicts the Bible on central issues such as the crucifixion, who Jesus is, the trinity, the Fatherhood of God, salvation, justice, forgiveness, and many other topics. (Surah 4:147;19:35;4:157;112:3;
5. Furthermore the Bible explicitly says that if any man or angel brings a message that is different, that man or angel is accursed by God and their message is false. (Gal 1:8)

So how do we deal with the fact that on one hand the Quran affirms the Bible as Allahs word, and relies of it for its own authenticity, yet on the other hand the Quran contradicts the Bible and the Bible rejects the Quran?

The simplest explanation is that the Quran is just the words of Muhammad, a fallible, sinful, regular man with little to no knowledge about what the Bible teaches, and he was simply wrong about the Bible.

But that would mean Islam is a false religion, so

This is the dilemma:

Either the Quran is correct in that the Bible is the true word of Allah. And if the Bible is the true word of Allah, then the Quran is false.

Or the Quran is just the words of a man, and therefore the Quran is false.

Either way, the Quran is false.