Arrange a little get to know one another type party. Just for the residents of this building. Serve some light fingerfood, and some wine too loosen yourself up and take it from there. Play some decent music and just start talking. Easiest thing in the world.
And do not invite by placing a written invitation on their doorstep, but go from door to door and discuss it/invite them in person. This will also serve as a form of introduction, so no matter the outcome of the invitation, it will be easier to start a conversation with them next time. Bring your roommate as moral support.