How to perform a for loop on each character in a string in Bash?

You can use a C-style for loop:

foo=string
for (( i=0; i<${#foo}; i++ )); do
  echo "${foo:$i:1}"
done

${#foo} expands to the length of foo. ${foo:$i:1} expands to the substring starting at position $i of length 1.