When you say "everything was fine", what do you mean? Did you manage to get WordPress up and running on the Ubuntu VM? How far did you get?
What files did you want to transfer? WordPress installation files? Or do you mean uploading files such as images for a post? The only time I've used an FTP server was when I needed to upload the WP installation files to a remote server. But if you're working on your local machine, you can either share a local folder to your virtual machine or download the files from the virtual machine and start the installation.
Regarding MAMP, never used it but there's some info about it on WordPress Codex and this article on Smashing Magazine could help.