Try this:
1:$ sudo mount /dev/sdb4 /mnt
2:$ for i in /sys /proc /run /dev; do sudo mount --bind "$i" "/mnt/$i"; done
3:$ sudo chroot /mnt
4:# grub-install /dev/sda
5:# update-grub
6:# exit
7:$ for i in /sys /proc /run /dev; do sudo umount "/mnt/$i"; done
8:$ exit
If you get an error on any line... let me know.