Connect to mysql in a docker container from the host

In a nutshell

I want to run mysql in a docker container and connect to it from my host. So far, the best I have achieved is:

ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

More details

I'm using the following Dockerfile:

FROM ubuntu:14.04.3
RUN apt-get update && apt-get install -y mysql-server

# Ensure we won't bind to localhost only
RUN grep -v bind-address /etc/mysql/my.cnf > temp.txt \
  && mv temp.txt /etc/mysql/my.cnf

# It doesn't seem needed since I'll use -p, but it can't hurt
EXPOSE 3306

CMD /etc/init.d/mysql start && tail -F /var/log/mysql.log

In the directory where there is this file, I can succesfully build the image and run it with:

> docker build -t my-image .
> docker run -d -p 12345:3306 my-image

When I attach to the image, it seems to work just fine:

# from the host
> docker exec -it <my_image_name> bash

#inside of the container now
$ mysql -u root
Welcome to the MySQL monitor.  Commands end with ; or \g.
[...]

However I don't have that much success from the host:

> mysql -P 12345 -uroot
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

Even more details

• I've seen that there's a question which looks like mine. However, it isn't the same (and it doesn't have any answers anyway)
• I've seen that there are images dedicated to mysql, but I didn't have more success with them
• My grep -v may feel weird. Admittedly, there may be cleaner way to do it. But when I attach my image, I can observe it actually worked as expected (ie: removed the bind-address). And I can see in the container /var/log/mysql/error.log:

Server hostname (bind-address): '0.0.0.0'; port: 3306 - '0.0.0.0' resolves to '0.0.0.0'; Server socket created on IP: '0.0.0.0'.

If you use "127.0.0.1" instead of localhost mysql will use tcp method and you should be able to connect container with:

mysql -h 127.0.0.1 -P 3306 -u root