ERROR: While executing gem ... (Gem::FilePermissionError) - ruby

Question

I'm trying to setup rbenv to use with fastlane. I follow the instructions here. I've installed rbenv
rbenv install 2.3.1
Then updated it so the version points to:
rbenv local 2.3.1 => 2.3.1 (set by /Users/pepe/Development/test-ios/.ruby-version)
I then try to install bundler:
gem install bundler and get the following error:
ERROR: While executing gem ... (Gem::FilePermissionError)
You don't have write permissions for the /Library/Ruby/Gems/2.0.0 directory.
And running following gives me:
rbenv which gem
/Users/pernillau-ext/.rbenv/versions/2.3.1/bin/gem
which gem
/Users/pernillau-ext/.rbenv/shims/gem
Obviously rbenv points to one installation of gem and the system (Mac OS X 10.116) comes with preinstalled ruby and gems which is installed in /Library/Ruby/Gems/2.0.0 directory. So, what am I missing here? Why is gem command using the wrong version.
EDIT:
My bash_profile:
export ANDROID_HOME=/Users/pepe/Library/Android/sdk
export JAVA_HOME=/Library/Java/JavaVirtualMachines/jdk1.8.0_102.jdk/Contents/Home
export GEM_PATH=/Users/pepe/.rbenv/versions/2.3.1/lib/ruby/gems/2.3.0
export PATH=$PATH:/Users/pernillau-ext/Library/Android/sdk/tools:/Users/pernillau-ext/Library/Android/sdk/platform-tools
PATH="$(perl -e 'print join(":", grep { not $seen{$_}++ } split(/:/, $ENV{PATH}))')"
eval "$(rbenv init -)"

Answer 1

Try mooving things in $PATH a little. Move rbenv to the front of the $PATH.
$PATH in your shell should look roughtly like (pseudocode):
{rbenv shims} : {rbenv bin} : {system paths}