Click on "Preferences" under the BitRocket drop-down menu:

Under the General button, ensure that "Display upload rate atop dock icon" is checked.
This will allow you to see if you are uploading files and then allow you to cancel them:

Under the "Transfers" button, limit uploads to 0 kb/s:

Under the "Network" button, uncheck (disable) the "Enable Peer Exchange" capability of the BitRocket client: