Dockerfile

FROM custom/ruby

ADD . /src
WORKDIR /src

# NB. I'm installing ruby with RVM, so I have to run these commands via bash to get rvm to start up
RUN /bin/bash -lc bundle install --deployment --path ./vendor

EXPOSE 80
ENTRYPOINT ["/bin/bash", "-lc", "bundle exec ruby serve.rb"]

Gemfile

source "https://rubygems.org"
ruby "2.0.0"

gem "sinatra"

serve.rb

require "sinatra"

set :port, 80

get "/" do
  "DEMO time"
end

z-output.sh

$ sudo docker build -t custom/demo .
Uploading context 10240 bytes
Step 1 : FROM custom/ruby
 ---> b0a81cbfbc4a
Step 2 : ADD . /src
 ---> d32b9263ff52
Step 3 : WORKDIR /src
 ---> Running in c61aacbe9d2a
 ---> 2f3591425c9c
Step 4 : RUN /bin/bash -lc bundle install --deployment --path ./vendor
 ---> Running in c6ac45dcfcd6
Fetching gem metadata from https://rubygems.org/...........
Fetching gem metadata from https://rubygems.org/..
Resolving dependencies...
Installing rack (1.5.2) 
Installing rack-protection (1.5.1) 
Installing tilt (1.4.1) 
Installing sinatra (1.4.4) 
Using bundler (1.3.5) 
Your bundle is complete!
Use `bundle show [gemname]` to see where a bundled gem is installed.
 ---> 959bf9d951e4
Step 5 : EXPOSE 80
 ---> Running in 633726f1efda
 ---> 16219e18d4ec
Step 6 : ENTRYPOINT ["/bin/bash", "-lc", "bundle exec ruby serve.rb"]
 ---> Running in abcca9b078e8
 ---> 5480ee01599a
Successfully built 5480ee01599a

$ sudo docker run -P custom/demo 
[2013-11-28 04:45:06] INFO  WEBrick 1.3.1
[2013-11-28 04:45:06] INFO  ruby 2.0.0 (2013-11-22) [x86_64-linux]
== Sinatra/1.4.4 has taken the stage on 80 for development with backup from WEBrick
[2013-11-28 04:45:06] INFO  WEBrick::HTTPServer#start: pid=1 port=80

# In a new terminal

$ sudo docker ps
CONTAINER ID        IMAGE                       COMMAND                CREATED             STATUS              PORTS                   NAMES
f3d2978b4d71        custom/demo:latest          /bin/bash -lc bundle   5 minutes ago       Up 5 minutes        0.0.0.0:49163->80/tcp   clever_galileo

$ curl 0.0.0.0:49163
curl: (56) Recv failure: Connection reset by peer

Results from netstat -tulpn:

Active Internet connections (only servers)
Proto Recv-Q Send-Q Local Address               Foreign Address             State       PID/Program name   
tcp        0      0 127.0.0.1:80                0.0.0.0:*                   LISTEN      7/ruby              
tcp        0      0 ::1:80                      :::*                        LISTEN      7/ruby 

And curl 0.0.0.0:80 gives "DEMO time" as expected.