Bash-script. Shift seconds

Unless the subtitle file spans more than 24 hours, you can use date for this:

#!/usr/bin/env bash

set -o errexit -o noclobber -o nounset -o pipefail

date_offset="$1"

shift_date() {
    date --date="$1 $date_offset" +%T,%N | cut -c 1-12
}

while read -r line
do
    if [[ $line =~ ^[0-9][0-9]:[0-9][0-9]:[0-9][0-9],[0-9][0-9][0-9]\ --\>\ [0-9][0-9]:[0-9][0-9]:[0-9][0-9],[0-9][0-9][0-9]$ ]]
    then
        read -r start_date separator end_date <<<"$line"
        new_start_date="$(shift_date "$start_date")"
        new_end_date="$(shift_date "$end_date")"
        printf "%s %s %s\n" "$new_start_date" "$separator" "$new_end_date"
        echo "New date"
    else
        printf "%s\n" "$line"
    fi
done

For some reason you need to use decimal numbers with this, but it works:

$ ./shifter.sh "+3.0 seconds" < bmt.srt
5
00:01:05,323 --> 00:01:08,572
New date
Hello, my frieds!
6

Perl solution. I did not use any classical time handling module, as miliseconds handling is generally poorly supported.

#!/usr/bin/perl
use warnings;
use strict;

use constant FACTORS => (60 * 60 * 1000,
                              60 * 1000,
                                   1000,
                                      1);

sub time2ms {
    my $time = shift;
    my ($ms, $i) = (0, 0);
    $ms += (FACTORS)[$i++] * $_ for split /[^0-9]/, $time;
    return $ms;
}


sub ms2time {
    my $ms = shift;
    my $str = q();
    for my $i (0 .. 3) {
        $str .= sprintf '%02d' . (':', ':', ',', q())[$i],
                        $ms / (FACTORS)[$i];
        $ms = $ms % (FACTORS)[$i];
    }
    return $str;
}


my $diff   = 1000 * shift;
my $TIME_R = qr/[0-9]{2}:[0-9]{2}:[0-9]{2},[0-9]{3}/;
while (<>) {
    if (my ($from, $to) = /($TIME_R) --> ($TIME_R)/) {
        my $i = 0;
        for my $time ($from, $to) {
            $time = time2ms($time) + $diff;
            print ms2time($time), (' --> ', "\n")[$i++];
        }
    } else {
        print;
    }
}