Bind mounts are easy to maintain and backup. However if you share data amongst multiple container docker volumes are recommend especially for managing state.

Backup volumes:

docker run --rm --volumes-from dbstore -v $(pwd):/backup containername tar cvf /backup/backup.tar /dbdata

• Launch a new container and mount the volume from the dbstore container
• Mount a local host directory as /backup
• Pass a command that tars the contents of the dbdata volume to a backup.tar file inside /backup directory.

docker docs - volumes

Database volume backup without stopping the service: bash into the container, dump it, and copy it out with docker cp. Run it periodically via crontab