If I'm understanding you correctly, something like the following might work. It would give you access to the data from the rows with the same ID in the other query.

my %ids;

# ...
$sth->bind_columns( undef, \$orig_service_id, \$orig_stop, $depart_ori
+g);
while ($sth->fetch())
{
    push @{$ids{$orig_service_id}}, {
        stop   => $orig_stop,
        depart => $depart_orig,
        # ...
    };
}

# ...
$sth->bind_columns( undef, \$dest_service_id, \$dest_stop, $depart_des
+t);
while ($sth->fetch())
{
    if (exists $ids{$dest_service_id}) {
        print "ID $dest_service_id:\n";
        my $i = 0;  # counter (only needed for demo purposes)
        for my $orig ( @{$ids{$dest_service_id}} ) {
            # $orig is a hashref to origin data
            printf "matching origin row #%d:\n", ++$i;
            printf "  orig_stop   = %s\n", $orig->{stop};
            printf "  depart_orig = %s\n", $orig->{depart};
            # ...
        }
    }
}
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