using random to generate a random string in bash

Use parameter expansion. ${#chars} is the number of possible characters, % is the modulo operator. ${chars:offset:length} selects the character(s) at position offset, i.e. 0 - length($chars) in our case.

chars=abcd1234ABCD
for i in {1..8} ; do
    echo -n "${chars:RANDOM%${#chars}:1}"
done
echo

Another way to generate a 32 bytes (for example) hexadecimal string:

xxd -l 32 -c 32 -p < /dev/random

add -u if you want uppercase characters instead.

For those looking for a random alpha-numeric string in bash:

LC_ALL=C tr -dc A-Za-z0-9 </dev/urandom | head -c 64

The same as a well-documented function:

function rand-str {
    # Return random alpha-numeric string of given LENGTH
    #
    # Usage: VALUE=$(rand-str $LENGTH)
    #    or: VALUE=$(rand-str)

    local DEFAULT_LENGTH=64
    local LENGTH=${1:-$DEFAULT_LENGTH}

    LC_ALL=C tr -dc A-Za-z0-9 </dev/urandom | head -c $LENGTH
    # LC_ALL=C: required for Mac OS X - https://unix.stackexchange.com/a/363194/403075
    # -dc: delete complementary set == delete all except given set
}