use strict;
use warnings;

# $leading_0s[$n] is a regex matching any byte that begins with at lea
+st $n '0' bits
my @leading_0s = (qr//, map {
    my $max = chr(0xFF >> $_);
    qr/[\0-$max]/;
} 1..8);

# $trailing_0s[$n] is a regex matching any byte that ends with at leas
+t $n '0' bits
my @trailing_0s = (qr//, map {
    my $step = 1 << $_;
    my @ok = map { chr($step * $_) } 0..0xFF >> $_;
    local $" = q[];
    qr/[\Q@ok\E]/
} 1..8);

# Test if a string contains $n consecutive '0' bits.
# If yes, returns the bit offset of the match.
# Otherwise, returns -1.
sub match_0s {
    my $n = shift; # number of consecutive '0' bits to be matched
    local $_ = shift || $_; # string to match against

    for my $trailing (0..8) {
        my $full = $n - $trailing >> 3;
        my $leading = $n - $trailing & 7;
        if (/$trailing_0s[$trailing]\0{$full}$leading_0s[$leading]/) {
            return $-[0] << 3 | -$trailing & 7;
        }
    }

    return -1;
}

$_ = "ABC`\0abc";
print match_0s(14), $/;        # 27
print match_0s(15), $/;        # -1
print match_0s(24, 0.0.0), $/; # 0
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Tested, but not benchmarked. It may or may not be faster that the straightforward approach using unpack. To change endianness, just switch @leading_0s and @trailing_0s.

EDIT: now works even when the string is made entirely of null bytes.

EDIT: doesn't work for $n < 8. This case is left as an exercise to the reader. (: