Persistent mysql data from docker container

How can I persist data from my mysql container? I'd really like to mount /var/lib/mysql from the container to the host machine. This indeed creates the directory, but when I create data, stop my application, and start a new one with the mounted directory, nothing is there. I've messed around with giving the directory all permissions and changing the user and group to root but nothing seems to work. I keep seeing people saying to use a data container, but I don't see how that can work with Amazon ec2 container service (ECS), considering each time I stop and start a task it would create a new data container rather than use an existing one. Please help. Thank you