How about something based on:

my $data = "1024 bytes of data from the file";
my $odd = "";
my $even = "";
for my $bitpair (0..(4 * length $data - 1)) {
  my $twobits = vec($data, $bitpair, 2);
  vec($odd, $bitpair, 1) = 1 if $twobits & 2;
  vec($even, $bitpair, 1) = 1 if $twobits & 1;
}
[download]

I might have odd and even backwards. Experiment to find out. This will turn 1024 bytes into two 512-byte strings.

I'm guessing your code is slow because you're carrying around a single bit as an entire scalar... huge amounts of data overhead.