Bye is such a strange word.
Neither the letter y or the letter e makes the sound of an i, yet when out next to each other only in this specific word they make an i sound.
Examples of that not happening are: yet, yes, yep, yeast, yesterday
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Well, Y can make an i sound. By, my, etc. With that in mind, thinking of y as a vowel, it makes sense. Usually when a vowel is followed by e it makes its letter sound. Aether, for example.