$ docker -v
Docker version 17.09.0-ce, build afdb6d4

$ docker run -i -t -d --name mysql_container mysql_image

$ docker run -i -t -d -v /home/ubuntu/mysql_data_dir:/var/lib/mysql --name mysql_container mysql_image

FROM ubuntu:16.04

RUN echo "mysql-server mysql-server/root_password password root" | debconf-set-selections
 && echo "mysql-server mysql-server/root_password_again password root" | debconf-set-selections

RUN apt-get update
 && apt-get install -y
    mysql-server
 && sed -i "s/127.0.0.1/0.0.0.0/g" /etc/mysql/mysql.conf.d/mysqld.cnf

COPY entrypoint.sh /entrypoint.sh
RUN chmod +x /entrypoint.sh

ENTRYPOINT ["/entrypoint.sh"]

EXPOSE 3306

CMD ["mysqld"]

#!/bin/bash
set -e

# Set users home directory
usermod -d /var/lib/mysql mysql

# Create dir for UNIX socket file
mkdir -p /var/lib/mysql /var/run/mysqld
chown -R mysql:mysql /var/lib/mysql /var/run/mysqld

mysqld_safe &

exec "$@"