Use ENTRYPOINT for stuff like this. Any CMD parameters are appended to the given ENTRYPOINT.
So, if you update the Dockerfile to:
FROM ubuntu:15.04
ENTRYPOINT ["/bin/bash", "-c", "cat"]
Things should work as you wish.
Also, as you don’t need the $1, you should be able to change it to:
FROM ubuntu:15.04
ENTRYPOINT ["/bin/cat"]
I haven’t tested any of this, so let me know if it doesn’t work.