None of the answers here worked for me, so I am writing a new one referencing https://pimylifeup.com/raspberry-pi-torrentbox/ which worked great for me and allowed me to run transmission as pi user to access my USB drive. This is not directly answering the OP but this question is very popular (first Google result) for this sort of problem so I put it here.
I found that the file system was the problem for me. Luckily it was a brand new usb hard drive so wasn't an issue to format it.
I first formatted the hard drive to ext4
sudo mkfs.ext4 /dev/<usb disk> -L <diskname>
Then I mounted the usb hard drive
sudo mount /dev/<usb disk> /mnt/<my mount folder>
Once mounted I changed the group ...