The next letter in the series "A Z E B I Y O" is "C." The reason for this can be understood by separating the series into three patterns: the vowels (A, E, I, O, U), the letters backward (Z, Y, X, ...), and consonants (B, C, D, ...).
The vowels in the series have the pattern "A _ E _ I _ O." The letters backward use the pattern "_ Z _ _ _ Y _." And lastly, the consonants follow the pattern "_ _ _ B _ _ _." Looking at these separate patterns, it can be seen that the eighth letter in the series cannot be a vowel, nor is it an "X" (not yet). Therefore, it is from the third series, the consonants, and following "B" is "C."