"For simplicity, assume that you are given the book content as a string"
Then, as we already have the string in memory we don't spend operations reading the contents into memory and we can go directly to count the number of occurrences.
In my opinion its valid to say that an integer operation can be executed in $O(1)$ that includes addition, subtraction, multiply, division and obviously binary comparison operations.
Modify the pointer to string to be a UINT64 array pointer
Iterate the array and for each element (representing 64 bits or 8 characters assuming 1 byte per character) execute a function that by using less than 8 integer binary comparisons accurately tell you how many 'As' are in the element structure.
let $M$ be the number of steps required by such function and $N$ the number of characters
Your supposed upper bound complexity will be then $O((N/8)*M)$
Obviously this is just a fake solution however it could fit real world and interviews are not theoretical exams, the interviewer were just trying to learn how you workout a problem, sometimes is not necessary to have a final valid solution but just show how capable are you to pursue a potential solution.