I could be wrong but couldn't you store a seperate permission int for each componenent giving 64 possible permissions per component. That way you still only store an int but a user may have X amount of permission int's depending on the number of components.
You could extend the basic permissions class when you create a component to provide methods(aliases) for your permissions that return a boolean value for each permission. I'm thinking along the lines of Class::DBI for your construction of objects, that way your classes/code need only grab the permissions for the components they are interested in.
some psuedo perl.
package main;
use User::Permissions;
use User::Permissions::Node;
use User::Permissions::Page;
my $up = User::Permissions->new(user_id => 1);
my $up_page = User::Permissions::Page->new;
warn "can read nodes" if User::Permissions::Node->read; # package call
warn "can read pages" if $up_page->read; # object call
# ... later ...
package Foo;
use User::Permissions;
use User::Permissions::Baz;
my $up = User::Permissions->new(user_id => 1);
warn "can write baz" if User::Permissions::Baz->write;