Docker container can't see a serial port device

You can check if the script described in "Notification of new USB devices in docker container" (from Guido Diepen -- gdiepen) can help.

He too runs his container with the --privileged argument to allow it to access the devices. And he mounts the host directory /dev/bus/usb to the /dev/bus/usb directory within the container with the argument -v /dev/bus/usb:/dev/bus/usb when starting said container.

The script uses both inotifywait and lsusb to wait for devices to be (un)plugged and check if it was the device we are interested in.

The inotifywait will keep on listening to inodes create/delete events under the dev/bus/usb directory and will execute commands whenever an inode corresponding to a relevant device has been just created.

See also, once you have detected an plugged USB device, How to get Bus and Device relationship for a /dev/ttyUSB (not related to Docker, but still relevant).