Gems are installed to the user location with:

$ gem install GEM_NAME --user-install

The directory install to will not be in the PATH variable.

Update path

Here is how to set it, such as in ~/.bashrc.

From SO answer.

This first checks that ruby and gem are installed and available, without printing. Note [[ is not needed.

if which ruby >/dev/null && which gem >/dev/null; then
  export PATH="$(ruby -r rubygems -e 'puts Gem.user_dir')/bin:$PATH"
fi

Breakdown

This runs the library (-r) named rubygems and sends a command to it puts Gem.user_dir to print the user gem directory as a full path.

$ echo "$(ruby -r rubygems -e 'puts Gem.user_dir')/bin"

Example:

/Users/mcurrin/.gem/ruby/2.6.0/bin

Test it:

$ gem install bundler --user-install

$ which bundler
/Users/mcurrin/.gem/ruby/2.6.0/bin/bundle