Just reiterating that for those (at least on OSX) for whom
gem install bundler
Gives a permissions error, an option that seems to have worked for many people is to use rbenv, which kind of adds a shim between your ruby commands (like gem install) and your environment (if my understanding is correct).
Definitely check out this answer.
The process is laid out fairly well under the above link. I chose to install via homebrew:
brew update
brew install rbenv
Then you have to add an argument command to your profile, which if you're using the common ~/.bash_profile, can be done with:
echo 'eval "$(rbenv init -)"' >> ~/.bash_profile
Which it looks like is adding a command to initialize rbenv via your shell.
Don't for get to start a new shell, possibly by opening a new terminal or using the source ~/.bash_profile command.
Make sure your $PATH has this .rbenv/shims BEFORE any other directory where your shell might be looking for Ruby (OSX comes with it's own version that we don't want to fiddle with): echo $PATH.
which ruby
/Users/mikekilmer/.rbenv/shims/ruby
#GOOD!
Now install a version of Ruby:
rbenv install 2.2.3 
(See all possible versions with rbenv install -l).
Now we can use rbenv global 2.2.3 to switch to a use the newer version of Ruby globally. (Hmm. I thought we didn't want to mess with the system version.) You could also try it with rbenv local 2.2.3 or rbenv shell 2.2.3.
Finally run:
rbenv rehash
Now ruby -v should return 2.2.3 and gem install bundler should work. 
Did here.