You would only need 5 bits because you are counting to 26 (if we take only upper or lowercase letters). 5 bits will count up to 31, so you’ve actually got more space than you need. You can’t use 4 because that only counts to 15.
If you want both upper and lowercase then 6 bits is your answer – 6 bits will happily count to 63, while your double alphabet has (2 * 24 = 48) characters, again leaving plenty of headroom.