Here's a helper function that executes a single shell command as sudo with a supplied password:
(defun sudo-shell-command (buffer password command)
(let ((proc (start-process-shell-command
"*sudo*"
buffer
(concat "sudo bash -c "
(shell-quote-argument command)))))
(process-send-string proc password)
(process-send-string proc "\r")
(process-send-eof proc)))
You might apply it to your situation like so:
(defun sudo-bundle-install (password)
(interactive (list (read-passwd "Sudo password for bundle install: ")))
(let ((default-directory (concat default-directory
"./fixtures/test-kitchen-mode-test-run/")))
(sudo-shell-command
"*test-kitchen-test-setup*"
password
"bundle install; bundle exec berks install")
(clear-string password)))