I ran into the exact same issue. The answer is actually deceptively simple. Since Mavericks now includes Ruby 2.0.0p247 and Rubygems 2.0.3, and you apparently upgraded, your system ruby will not find your bundler or ansi gems. So what you need to do is install both with your system ruby, as root.
sudo /usr/bin/gem install bundler
sudo /usr/bin/gem install ansi
Then just restart or terminal. You can now run boxen
as you would normally. Also, in order not to keep old files lying around, you may want to cleanup /Library/Ruby/Gems/1.8/
because it will include your old installation of both bundler and ansi on a ruby and gem installation you no longer have.