How do I mount --bind inside a Docker container?
For using the mount system call, you need the CAP_SYS_ADMIN capability. By default, Docker drops all capabilities when spawning a container (meaning that even as root, you're not allowed to do everything). See the mount(2) man page for more information.
You can start your container with the --cap-add=SYS_ADMIN flag to add this capability to your container:
root@host > docker run --rm -it --cap-add=SYS_ADMIN debian:jessieroot@ee0b1d5fe546:/# mkdir /mnt/testroot@ee0b1d5fe546:/# mount --bind /home /mnt/test/root@ee0b1d5fe546:/# Use this with caution. Do not run untrusted software in a privileged container.