I just could not leave this to rest. There might be more optimizations possible, but at least it offers you 5 native perl methods to do it and the speed diff:

$ cat test.pl
use strict;
use warnings;

use Data::Peek;
use Benchmark qw( cmpthese );

my $src = pack "C*" => map { int rand 256 } 0 .. 3071;

print STDERR "First 48 bytes of the compressed data ...\n";
DHexDump substr $src, 0, 48;

for (unpack "(a3)*", substr $src, 0, 12) {
    DHexDump $_;
    my $bits = unpack "B*", $_;
    (my $b8 = substr $bits, 0, 48) =~ s/(.{8})/$1 /g;
    (my $b6 = substr $bits, 0, 48) =~ s/(.{6})/$1 /g;
    print STDERR "      $b8\n      $b6\n";
    }

# unpack pack unpack unpack reverse
sub upuu
{
    map { unpack "C", pack "b6", scalar reverse $_ }
        unpack "(a6)*" => unpack "B*" => $src;
    } # opuu

# unpack with 00
sub upuu0
{
    map { unpack "C", pack "B8", "00$_" }
        unpack "(a6)*" => unpack "B*" => $src;
    } # opuu0

# using uuencode
sub uu
{
    map { map { ($_ - 32) & 63 } unpack "xC*" => $_ }
        split m/ *\n/ => pack "u" => $src;
    } # uu

{   my @lut;
    for (0 .. 0b111111) {
        $lut[$_ << 18] = $_;
        $lut[$_ << 12] = $_;
        $lut[$_ <<  6] = $_;
        $lut[$_      ] = $_;
        }

    sub mlut
    {
        map { my $v = unpack "N", "\00$_\x00\x00";
            ($lut[$v & 0b111111_000000_000000_000000],
             $lut[$v & 0b000000_111111_000000_000000],
             $lut[$v & 0b000000_000000_111111_000000],
                  $v & 0b000000_000000_000000_111111);
            } unpack "(a3)*" => $src;
        } # mlut
    }

# And shift unpack
{   my $m0 = 0b111111_000000_000000_000000;
    my $m1 = 0b000000_111111_000000_000000;
    my $m2 = 0b000000_000000_111111_000000;
    my $m3 = 0b000000_000000_000000_111111;
    sub asu
    {
        map {my $b = unpack "N", "\x00$_\x00\x00"; (
            ($b & $m0) >> 18,
            ($b & $m1) >> 12,
            ($b & $m2) >>  6,
            ($b & $m3)
            ) } unpack "(a3)*" => $src;
        } # asu
    }

my @dst;

@dst = uu ();
print STDERR "$#dst E\n";
print STDERR "uu:    (@dst[0..22] ...\n        @dst[4073..4095])\n";
@dst = upuu  ();
print STDERR "upuu:  (@dst[0..22] ...\n        @dst[4073..4095])\n";
@dst = upuu0 ();
print STDERR "upuu0: (@dst[0..22] ...\n        @dst[4073..4095])\n";

@dst = asu ();
print STDERR "asu:   (@dst[0..22] ...\n        @dst[4073..4095])\n";
@dst = mlut ();
print STDERR "mlut:  (@dst[0..22] ...\n        @dst[4073..4095])\n";

cmpthese (-2, { uu => \&uu, upuu => \&upuu, upuu0 => \&upuu0, asu => \
+&asu, mlut => \&mlut });
$

$ perl test.pl
First 48 bytes of the compressed data ...
0000  1c 66 02 ac 50 1f 41 b2  e4 10 b9 03 38 b3 7e 2d  .f..P.A.....8.
+~-
0010  5e 95 02 c6 c7 71 39 08  c7 82 37 40 0d 40 c1 e1  ^....q9...7@.@
+..
0020  1f 9a d9 6d 51 f3 7e 0a  8d 9b 75 85 0a a5 82 65  ...mQ.~...u...
+.e
0000  1c 66 02                                          .f.
      00011100 01100110 00000010
      000111 000110 011000 000010
0000  ac 50 1f                                          .P.
      10101100 01010000 00011111
      101011 000101 000000 011111
0000  41 b2 e4                                          A..
      01000001 10110010 11100100
      010000 011011 001011 100100
0000  10 b9 03                                          ...
      00010000 10111001 00000011
      000100 001011 100100 000011
4095 E
uu:    (7 6 24 2 43 5 0 31 16 27 11 36 4 11 36 3 14 11 13 62 11 21 58 
+...
        23 32 30 37 37 26 19 30 42 19 29 32 54 2 9 3 23 32 62 52 5 31 
+46)
upuu:  (7 6 24 2 43 5 0 31 16 27 11 36 4 11 36 3 14 11 13 62 11 21 58 
+...
        23 32 30 37 37 26 19 30 42 19 29 32 54 2 9 3 23 32 62 52 5 31 
+46)
upuu0: (7 6 24 2 43 5 0 31 16 27 11 36 4 11 36 3 14 11 13 62 11 21 58 
+...
        23 32 30 37 37 26 19 30 42 19 29 32 54 2 9 3 23 32 62 52 5 31 
+46)
asu:   (7 6 24 2 43 5 0 31 16 27 11 36 4 11 36 3 14 11 13 62 11 21 58 
+...
        23 32 30 37 37 26 19 30 42 19 29 32 54 2 9 3 23 32 62 52 5 31 
+46)
mlut:  (7 6 24 2 43 5 0 31 16 27 11 36 4 11 36 3 14 11 13 62 11 21 58 
+...
        23 32 30 37 37 26 19 30 42 19 29 32 54 2 9 3 23 32 62 52 5 31 
+46)
        Rate upuu0  upuu  mlut   asu    uu
upuu0  354/s    --   -1%  -56%  -64%  -68%
upuu   357/s    1%    --  -56%  -64%  -67%
mlut   813/s  130%  128%    --  -17%  -26%
asu    985/s  178%  176%   21%    --  -10%
uu    1093/s  209%  206%   34%   11%    --
$
[download]

Enjoy!