I have pathogen installed, which does basically the same thing as Vundle.
Just clone the git repo to your ~/.vim/bundle directory and continue compiling as instructed.
cd ~/.vim/bundle
git clone https://github.com/Valloric/YouCompleteMe.git
cd YouCompleteMe
mkdir ycmbuild
cd ycmbuild
# Do this only if you don't have cmake installed
brew update
brew install cmake
cmake -G "Unix Makefiles" . ~/.vim/bundle/YouCompleteMe/cpp/
make ycm_core
<Restart vim>