Newer processors have a popcnt ("population count") instruction, which computes the number of 1-bits (for up to 64 bits) with a single fast CPU instruction.  In other words, if you want real speed at the cost of portability, you could hack a little assembly^1,2.

A quick test shows that this is roughly 10 times as fast as the above mentioned unpack "%32b*".

#!/usr/bin/perl -wl
use strict;

use Inline C => Config =>
           LDDLFLAGS => '-shared ../../../popcount.o';
use Inline "C";
use Benchmark "cmpthese";

my $s = pack "C*", map { int rand 256 } 1 .. 2**18;  # 256k

#print unpack q/%32b*/, $s;
#print count_bits($s);

cmpthese (-2, {
    unpack => sub { my $n = unpack q/%32b*/, $s; },
    popcnt => sub { my $n = count_bits($s); },
});

__END__
__C__
extern unsigned long popcount(char *, int64_t);  // the asm routine

unsigned long count_bits (SV* bitstr) {  // XS wrapper
    STRLEN l;
    char *s = SvPV(bitstr, l);
    return popcount(s, l);
}
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          Rate unpack popcnt
unpack  1252/s     --   -91%
popcnt 13581/s   984%     --
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Tested with

$ cat /proc/cpuinfo | grep name | head -1
model name    : AMD Phenom(tm) 9600 Quad-Core Processor
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___

¹ The assembly code (nasm syntax; 64 bit; gcc register subroutine calling convention — compile with nasm -f elf64 popcount.asm ):

bits 64
global popcount
section .text

; prototype: unsigned long popcount(char*, int64_t);
popcount:
        push rbp
        mov rbp, rsp
        mov rcx, rsi
        shr rcx, 3
        mov rsi, rdi
        xor rax, rax

.cnt    popcnt rbx, [rsi]
        add rax, rbx
        add rsi, 8
        loop .cnt
          
        mov rsp, rbp
        pop rbp
        ret
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(Caveat: as this is just proof of concept code, the string length is assumed to be a multiple of 8 byte/64 bit, so you might need to zero-pad it)

² In theory, there is also the gcc __builtin_popcount function, but in practice it turns out to be less portable than a piece of assembly code.