at first, the best option for static local networks is the "bridged" option, in virtualbox network settings. second, you better setup all network interfaces with static config and not the crappy DHCP. after doing that, install samba (to both Tiny setting it as "onboot" and ubuntu) and also install some decent filemanager to Tiny (e.g. pcmanfm2). go to the folder you want to share in ubuntu, right click and select the "sharing options". enable the "share this folder" option and below that also enable the "allow other to write in this folder" option and click on the button "create share". close the dialog and that's it.
after that you can go to Tiny open the filemanager and write this "smb://xxx.xxx.xxx.xxx" (xxx.xxx.xxx.xxx is ubuntu IP) in the locationbar
you should see your shared folder among others (crap! how can i make these things smaller?)
double click your shared folder and now the authentication dialog appears
put you ubuntu username and password and connect. now you should see your files (now you can do whatever you want with them). to disconnect close the filemanager, click on the exit button, and select to exit to prompt. when on prompt, type "exit" and hit enter (to logoff your acount and close the smb connection). to logon just type "tc" and hit enter.