Is there a way to calculate a field in ArcMap to be one letter up from another field? I'll never need to go beyond letter 'T', so no worries there.
Field Ltr| Field NLtr a b b c
You can use this Python code expression:
chr( ord( !FIELD_NAME! ) + 1)
Note: Be aware to change the default parser from vbScript to Python
 after the attribute is intended to return only the 1st character of the input string, then, even if you have only a space after the 1st letter, you are sure that only one character is returned.
ord function returns the integer corresponding to the given character in the character table. By incrementing that value by one, you get the integer value corresponding to the next character. Then you use the inverse function
chr to get the character from the given integer.