ken@titan ~/tmp
$ cat > pm_11133222_rcfile
. ~/.bashrc
cd ~/tmp/pm_11133222_test_dir

##</code><code>##

#!/usr/bin/env perl

use strict;
use warnings;
use autodie ':all';

my @commands = (
    'set -vx',
    'pwd',
    "cd $ENV{HOME}",
    'pwd',
    'date',
    "/usr/bin/bash --rcfile $ENV{HOME}/tmp/pm_11133222_rcfile -i",
);

system qw{/usr/bin/xterm -e}, join ';', @commands;

##</code><code>##

+ pwd
/home/ken/tmp
+ cd /home/ken
+ pwd
/home/ken
+ date
Wed,  2 Jun 2021 16:38:27
+ /usr/bin/bash --rcfile /home/ken/tmp/pm_11133222_rcfile -i

ken@titan ~/tmp/pm_11133222_test_dir
$