PonyChat uses ZNC for its bouncer. This is how we do it.
$ docker build -t ponychat/znc .
$ docker volume create --name bnc-data
$ docker run --rm -itv bnc-data:/home/bnc/.znc alpine:3.4 sh -c 'chmod a+rwx /home/bnc/.znc'
$ docker run \
-e ATHEME_SERVER="ip:port" \
-e IRC_NETWORK_NAME="FooNet" \
-e IRC_NETWORK_DOMAIN="foo.net" \
-p 6697:6697 -v bnc-data:/home/bnc/.znc \
ponychat/znc