How to make RVM hook into bash 4.0's 'autocd' option and run .rvmrc

Question

I would like to know if there is a way to get RVM to work with Bash's autocd option. Manual cd commands execute the .rvmrc, but autocd does not.

What currently happens:

# (in ~/src, with ruby 1.8.7)
$ cd ~/src/my_project                       # use 'cd' command
Using /home/user/.rvm/gems/ruby-1.9.2-p290  # runs .rvmrc
~/src/my_project [1.9.2-p290] $             # ruby version is changed.

# (in ~/src, with ruby 1.8.7)
$ ~/src/my_project                          # (use autocd to change directory)
cd /home/ndbroadbent/src/rails/clockit/     # (autocd kicks in)
~/src/my_project [1.8.7] $                  # .rvmrc is ignored.