Drives automatically mounted under /media/user (or /run/media on certain distributions) cannot be read (or written) by any user other than the user, typically. This is because this location is managed by udisks2 and has Access Control Lists (ACLs) associated applied to it.
The recommended way to mount external drives is described here:
If you carefully follow that guide to mount your disk, Plex will be able to access it.
There is another method, which I don’t necessarily recommend. You can try modifying the ACLs for the auto-mount home for your user to allow Plex access. To do so, run the following command:
sudo setfacl -m u:plex:rx /media/bj/
This will give user plex read and execute permissions to the bj directory, under which your disk is being mounted. I’ve only tested this under Ubuntu. You should probably just use the method described in the linked thread to set up permanent mounts though.
