The easiest thing to install (or re-install, or repair) GRUB2 on your image is to use another VM running Linux. The alternative, the answer by toh, is rather complicated. If you boot a Linux VM, having plugged into it also your new disk image (besides the VM's own disk), it will be treated not as a file but as a real disk, bypassing the need for the device mapper (see link above).
So, boot another Linux VM, mount your new vdi disk,
mount /dev/sdb1 /mnt
and chroot into it:
mount -o bind /proc /mnt/proc mount -o bind /sys /mnt/sys mount -o bind /dev /mnt/dev cd /mnt; chroot .
Now you can install grub as follows
grub-install /dev/sdb update-grub /dev/sdb
then leave the chroot
environment (by means of `exit' or Ctrl+D, and
umount /mnt/dev umount /mnt/proc umount /mnt/sys umount /mnt
Your new vdi disk is now bootable, and can be used as the disk of a new Linux VM.