First of all, my code doesn't do $N < 8 ... so you'd only expect to see correct answers from 5 on down.

Obvious. (Once someone kindly points it out.)

I'm getting the correct numbers for 14..17 when I run it so I'm guessing there's something else going on with either your testbed or mine

Indeed, mine! (A dumb typo.)

C:\test>b-zeroBits.pl -N=1e5
Name "main::N" used only once: possible typo at C:\test\b-zeroBits.pl 
+line 1.
0100100010000100000100000010000000100000000100000000010000000000100000
+00000010000000
wrog: 1 : 0
wrog: 2 : 14
wrog: 3 : 5
wrog: 4 : 14
wrog: 5 : 14
wrog: 6 : 20
wrog: 7 : 27
wrog: 8 : 35
wrog: 9 : 44
wrog: 10 : 54
wrog: 11 : 65
wrog: 12 : 77
wrog: 13 : 90
wrog: 14 : 104
wrog: 15 : 119
wrog: 16 : 135
wrog: 17 : 152
[download]

My only excuse is attempting to give timely response to your efforts, whilst also construct a descent testbed and benchmark for 4 different approaches (3 posted + my own.). My own attempt -- essentially based on the ideas in the OP -- is proving to be a pain to code.

ok, well, here's a version that does all $N. The one caveat is it doesn't necessarily return the first match, the main problem with the (or at least my) regexp approach being that when you have a bunch of '|' alternatives and more than one matches, you can't control which one gets used.

Anyway, here's the code:

use strict;
use warnings;
no warnings 'redefine';

# $cc[$n]->[$k] is a character class matching a byte with
# a run of zero bits of length at least $k and starting
# exactly $n bits from the end

our @cc = map {
   my $n = $_;
   [ ($n==0 ? () : $n==8 ? ('') : (undef)),
     map {
      # $m = first bit after the start of the run
      #  that does not have to be zero
      my $m = $_+8-$n; 
      local $" = '';
      qr{[@{[map { 
                quotemeta(chr(0x80>>$n|$_<<$m)) . 
                ($n<7 ? '-' . quotemeta(chr(0xFF>>$n|$_<<$m)) : '')
             } 0..(0xFF>>$m)]}]}
     } ($n==0 ? 0 : 1)..$n ]
} 0..8;
$cc[0]->[0] = qr{^|$cc[0]->[0]"};


sub zero_bit_regexp {
  my $N = shift;
  my $p = join '|',
      map { $N<=$_ ? "$cc[$_]->[$N]()" :
                     "$cc[$_]->[$_](\\0{@{[($N-$_)>>3]}}$cc[8]->[($N-$
+_)&0x7])" }
          0..7;
  return qr{$p};
}

sub match_0s_w {
    my $N    = shift;       # number of consecutive '0' bits to be mat
+ched
    local $_ = shift || $_; # string to match against
    return ($_ !~ zero_bit_regexp($N)) ? -1 : $-[$#-]*8 - $#- + 1
}
[download]

which gives

1:  0
2:  5
3:  5
4:  14
5:  14
6:  20
7:  27
8:  35
9:  44
10:  54
11:  65
12:  77
13:  90
14:  119
15:  119
16:  135
17:  -1
[download]

where the results for 2, 4, and 14 are technically correct but unexpected