Apple's Final Cut Pro suite comes with helpful application for uploads: Compressor. It has built-in FTP support, which allows you to upload your Final Cut edits and Motion composites directly to Bits on the Run.
When publishing files through Bits on the Run, your original video should be of the highest quality possible. This ensures that Bits on the Run can generate various smaller transcodes of your video tuned for bitrate switching and mobile phones.
If your content is in HD, you could use a preset that encodes your edit to H264 (MP4/MOV) video at 720p with a datarate of 5000kbps. For SD video, you could use a slightly lower bitrate (e.g. 3000 kbps). For audio, use AAC with a bitrate of e.g. 256 kbps.
Regardless, do not use Apple Pro Res (since we don't support it) or an uncompressed video format (risk of upload timing out).
Next comes the actual shortcut of letting Compressor immediately upload your files. Add a new destination, and choose remote. The destination inspector will open and you will be able to add your FTP information:

At this point, the compressor will encode your files to a high-quality intermediate and then immediately upload the videos to Bits on the Run. Next, Bits on the Run will archive this intermediate video and transcode web-optimized versions of it (180p, 270p, 480p, 720p).