What does the Bible say about Transubstantiation?

Nothing.

Transubstantiation is a big word that means changing one substance to another.  The word itself is never found in Scripture because the word had not yet been coined.  That wouldn't happen for many more centuries.

However, there are examples of transubstantiation in the Bible.  Jesus Christ transubstantiated water into wine in the Wedding at Cana.

And Jesus Christ transubstantiated bread into His Body and wine into His Blood in the Last Supper.

Matthew 26:26 And as they were eating, Jesus took bread, and blessed it, and brake it, and gave it to the disciples, and said, Take, eat; this is my body.27 And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it;28 For this is my blood of the new testament, which is shed for many for the remission of sins.