That's quite a lot of superfluous effort. Integers are 32-bit only, but strings can have as many bits as you want. Use vec.

use constant FOO  => 0;
use constant BAR  => 1;
use constant BAZ  => 2;
use constant QUUX => 452;

sub permits {
    my $self = shift;
    vec( $self->{perms}, $_, 1 ) or return for @_;
    return 1;
}


# and later

if( $user->permits( FOO, BAR, BAZ ) ) {
    # ...
}
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Makeshifts last the longest.