I’ve been using rbenv for development for a while, but recently I started working with using rbenv on my Webfaction hosting. Here is a basic tutorial.
First, create a new Passenger app in the Webfaction control panel. You can create a Rails app, but it adds some extra cruft you don’t need.
Log into the server, and install rbenv locally, using the standard rbenv tutorial. You will want to also install ruby-build in order to set up your ruby versions. Compile and install the desired version of Ruby using rbenv install 2.2.2 (change the version to match).
I suggest that you update rubygems and install bundler at this point by switching to the desired version of ruby (rbenv global 2.2.2), and running gem update --system and gem install bundler. You may want to switch back to system Ruby, although this is up to you (rbenv global system).
In the app directory (webapps/yourappname), edit the Nginx config file at nginx/conf/nginx.conf. Set passenger_ruby to be /home/[yourusername]/.rbenv/shims/ruby.
After a restart, you should be running on your rbenv ruby.