Accessing array index variable from bash shell script loop?

You can do this using indirection. From the bash manpage:

If the first character of parameter is an exclamation point (!), it introduces a level of variable indirection. Bash uses the value of the variable formed from the rest of parameter as the name of the variable; this variable is then expanded and that value is used in the rest of the substitution, rather than the value of parameter itself. This is known as indi‐ rect expansion. The exceptions to this are the expansions of ${!prefix*} and ${!name[@]} described below. The exclama‐ tion point must immediately follow the left brace in order to introduce indirection.

For your example:

#!/bin/bash
AR=('foo' 'bar' 'baz' 'bat')
for i in "${!AR[@]};" do
  printf '${AR[%s]}=%s\n' "$i" "${AR[i]}"
done

This results in:

${AR[0]}=foo
${AR[1]}=bar
${AR[2]}=baz
${AR[3]}=bat

Note that this also work for non-succesive indexes:

#!/bin/bash
AR=([3]='foo' [5]='bar' [25]='baz' [7]='bat')
for i in "${!AR[@]};" do
  printf '${AR[%s]}=%s\n' "$i" "${AR[i]}"
done

This results in:

${AR[3]}=foo
${AR[5]}=bar
${AR[7]}=bat
${AR[25]}=baz