How can I access the virtual machine filesystem from within Windows?
Create shared folders from Virtual Box Manager. For each drive you will have to create a shared folder. These shared folder will appear in guest OS as network file-systems.

As Ubuntu (Linux) is underlying in QuickStart.

Mounting temporarily need to fire this command from terminal:

sudo mount.vboxsf [share_name] [directory - mount point e.g. /mnt/share/]


OR

sudo mount -t vboxsf [share_name] [directory - mount point e.g. /mnt/share/]


Mounting permanently using fstab (/etc/fstab)
Make sure to install samba first (in ubuntu it should be already installed or do it sudo apt-get install samba, it needs internet connection)  

Now edit your fstab file and add an entry in the last  

\\vboxsvr\[share_name] [directory - mount point e.g. /mnt/share/] vboxsf rw,gid=100,uid=1000,auto 0 0