You will need to exec bash.

use strict;
my $shell='/bin/bash'; #full path to bash here
$ENV{PATH}.=":/usr/local:/usr/local/bin:/usr/ccs:/usr/ccs/bin:/usr/ucb
+";
exec $shell;
#exec $shell '-bash'; #if you want to pretend to be a login shell
[download]

Also I am using perl to setup the path since no reason to call out for that since the bash will inherit perls version of the PATH.