Mounts and shared volumes are fine, if you can guarantee that the container is going to be scheduled on this specific machine, where the given filesystem lives.

If you can't guarantee that, you are going into the world of NFS (which databases do not like much) or iSCSI, or, if you have distributed storage, into the world of glusterfs, ceph or something similar.

It's much simpler to just set up a database server (or cluster) and live with that.