Can I use wifi or Bluetooth to get the same kind of connection to my phone that I can with USB? I have a new Samsung Galaxy S5 running Android 4.4.2, and I also have a laptop and desktop computer, both running Ubuntu 14.04. In order to access or transfer files from phone to computer, I can connect my Samsung by USB easily enough, but I thought I might be able to do something a little cooler using either wifi or Bluetooth.

My phone always connects to my home LAN whenever I'm at home, so if there was a way to make it appear on the network automatically every time it was in range, that would be sweet.

My laptop I'm often using at hotspots where I probably couldn't connect them via the LAN. So maybe for my laptop, some kind of Bluetooth connection would be best. I'm actually typing right now on my laptop, and I paired the phone and laptop together, so I can select to "Send files" from the laptop to the Android, but that's about as convenient as emailing it to myself. I really want to be able to open the Android internal SD drives like they were drives on a network.

This could be two questions, one about connecting my desktop by wifi and one about connecting my laptop by bluetooth, but I'm asking them together because it may be that maybe one approach works best for both scenarios. Or maybe I have it reversed and wifi would be better for the laptop and Bluetooth for the desktop.

In short, what is the best wireless way for me to make my Android phone always available to my computers so that I can transfer and access files to it? I'd ideally like to have the drives show up the same way they do as when connected by USB, so that I can do other things like syncing my music collection (with Banshee or Clementine) and possibly other tasks.
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.