A shared folder is not the great way if you want to automate backups to your Mac

Instead enable SSH on the Mac on and transfer your backups over it.

Go into System Preferences’. Under ‘Internet & Networking’ there is a ‘Sharing’ icon. Run that. In the list that appears, check the ‘Remote Login.

Since you want to use automation. this will serve quite good.

Here is an example of how copy a folder from your Ubuntu computer to your mac

rsync -azvr /path/to/source/folder MAC:/path/to/where/you/want/to/saveit/

where MAC is the ip address of your mac
the good thing with rsync that if you re-run this command it will only copy the changed files from the source directory over to your mac saving time and bandwidth.

the z flag adds compression. If you are copying a lot of already compressed files like movies, images or mp3s you don't gain any speed in using it

If you still want some kind of drive mapping so you can browse the computer from GUI.
It can also be done over ssh with the help of sshfs

on your Ubuntu computer install sshfs. Then add your user to the fuse group and finally mount the remote server

from terminal:

sudo apt-get install sshfs # install sshfs

mkdir macfolder 

sshfs username@MAC:/ macfolder

will mount your mac root filesystem under the folder macfolder