SQLAlchemyからSSHでEC2の踏み台サーバを経由してAWS RDSのデータを参照したい。

前提・実現したいこと

ここに質問の内容を詳しく書いてください。
SQLAlchemy(Dockerコンテナ内で実行)からAWS RDSのデータを参照しようとしています。
SSHでEC2の踏み台サーバを通してDB(MySQL)サーバのデータを取得しようとしたときにエラーが発生します。

発生している問題・エラーメッセージ

sqlalchemy.exc.OperationalError: (_mysql_exceptions.OperationalError) (2006, "Can't connect to MySQL server on 'DB_HOST' (111)") (Background on this error at: http://sqlalche.me/e/e3q8)

該当のソースコード

Dockerfile
FROM ubuntu:16.04

USER root
ENV HOME=/root
ARG PYTHON_VERSION=3.6.7
ARG PYTHON_ROOT=$HOME/local/python-$PYTHON_VERSION
ENV PATH=$PYTHON_ROOT/bin:$PATH

ARG PYENV_ROOT=$HOME/.pyenv
RUN apt-get update && apt-get -y upgrade
RUN apt-get -y install \
    git \
    make \
    build-essential \
    libssl-dev \
    zlib1g-dev \
    libbz2-dev \
    libreadline-dev \
    libsqlite3-dev \
    wget \
    curl \
    llvm \
    libncurses5-dev \
    libncursesw5-dev \
    xz-utils \
    tk-dev \
    libffi-dev \
    liblzma-dev
RUN git clone https://github.com/pyenv/pyenv.git ~/.pyenv
RUN $PYENV_ROOT/plugins/python-build/install.sh
RUN /usr/local/bin/python-build -v $PYTHON_VERSION $PYTHON_ROOT
RUN rm -rf $PYENV_ROOT

RUN pip install --upgrade pip

RUN /bin/bash -c "debconf-set-selections <<< 'mysql-server mysql-server/root_password password MY_PASSWORD'" && \
    /bin/bash -c "debconf-set-selections <<< 'mysql-server mysql-server/root_password_again password MY_PASSWORD'" && \
    apt install -y mysql-server libmysqlclient-dev
VOLUME /var/run/mysqld
COPY bash_profile /root/.bash_profile
RUN pip install sshtunnel mysqlclient sqlalchemy

RUN pip install pandas

ARG WORKDIR=$HOME/app
VOLUME $WORKDIR
WORKDIR $WORKDIR

bash
# bash_profile
touch /var/run/mysqld/mysqld.sock
chown -R mysql:mysql /var/run/mysqld /var/lib/mysql
service mysql start
chmod 600 ./.ssh/*

$ docker run -v $(pwd):/root/app -it IMAGE_NAME bash --login

db.py
from sshtunnel import SSHTunnelForwarder
import sqlalchemy
import pandas as pd

SSH_HOST = 'SSH_HOST_IP'
SSH_PORT = 22
SSH_HOST_KEY = None
SSH_USERNAME = 'ec2-user'
SSH_PASSWORD = None
SSH_PKEY = './.ssh/my.pem'
DB_HOST = 'hoge.rds.amazonaws.com'
REMOTE_BIND_ADDRESS = (DB_HOST, 3306)
DB_USER = 'DB_USERNAME'
DB_PASSWORD = 'DB_PASSWORD'
DB_PORT = 3306
DB_NAME = 'db'

with SSHTunnelForwarder(SSH_HOST, SSH_PORT, ssh_host_key=SSH_HOST_KEY,
                        ssh_username=SSH_USERNAME, ssh_password=SSH_PASSWORD,
                        ssh_pkey=SSH_PKEY,
                        remote_bind_address=REMOTE_BIND_ADDRESS) as server:
    con = sqlalchemy.create_engine(
        f'mysql+mysqldb://{DB_USER}:{DB_PASSWORD}@{DB_HOST}:{DB_PORT}/{DB_NAME}')
    data = pd.read_sql('SQL_QUERY', con)