Integer ASCII value to character in BASH using printf

One line

printf "\x$(printf %x 65)"

Two lines

set $(printf %x 65)printf "\x$1"

Here is one if you do not mind using awk

awk 'BEGIN{printf "%c", 65}'

This works (with the value in octal):

$ printf '%b' '\101'A

even for (some: don't go over 7) sequences:

$ printf '%b' '\'{101..107}ABCDEFG

A general construct that allows (decimal) values in any range is:

$ printf '%b' $(printf '\\%03o' {65..122})ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz

Or you could use the hex values of the characters:

$ printf '%b' $(printf '\\x%x' {65..122})ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz

You also could get the character back with xxd (use hexadecimal values):

$ echo "41" | xxd -p -rA

That is, one action is the reverse of the other:

$ printf "%x" "'A" | xxd -p -rA

And also works with several hex values at once:

$ echo "41 42 43 44 45 46 47 48 49 4a" | xxd -p -rABCDEFGHIJ

or sequences (printf is used here to get hex values):

$ printf '%x' {65..90} | xxd -r -p ABCDEFGHIJKLMNOPQRSTUVWXYZ

Or even use awk:

$ echo 65 | awk '{printf("%c",$1)}'A

even for sequences:

$ seq 65 90 | awk '{printf("%c",$1)}'ABCDEFGHIJKLMNOPQRSTUVWXYZ

For your second question, it seems the leading-quote syntax (\'A) is specific to printf:

If the leading character is a single-quote or double-quote, the value shall be the numeric value in the underlying codeset of the character following the single-quote or double-quote.

From https://pubs.opengroup.org/onlinepubs/9699919799/utilities/printf.html