Can I use wifi or Bluetooth to get the same kind of connection to my phone that I can with USB?
Probably you can create a Tasker profile to connect to the Wifi network automatically when you arrive at home (or the home Wifi network is in the range) 
Another good thing you can achieve it using rSync backup is that, you can use rSync and use a Tasker job to periodically (or conditionally) upload/download data from/to your phone. You can refer to rSync's documentation for its configuration and other setup steps. You can configure it to only specify required one way transfer of files.