The answer you are seeking is vec.

This snippet prints a bit string (as a string rather than a number as your number could be 128-bits which would move into the realms of floating point inaccuracies), consisting of the value of the 49th through 69th bits, of the 6, 543, 210th 128-bit chunk of a 100MB string.

open F, '<', 'e:\100MB' or die $!;
binmode F;
{ local $/ = \(100*1024*1024); $data = <F> };

sub bits_of_chunk{
    my( $chunk, $start, $end ) = @_;
    join'', map{ 
        vec $data, $_, 1 
    } ($chunk * 16 * 8 + $start)
      .. 
      ($chunk * 16 * 8 +$end);
};

print bits_of_chunk( 6543210, 49, 69 );

000000000000000000000
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The bits are accessed directly from the 100MB string and are return very quickly.