I’ve found a couple links you might have useful.
The first is a community thread Has anyone passed data from Edison to a phone via Bluetooth? that discusses passing data from Edison to Bluetooth.
The second one is about Connecting the Intel® Edison board to your Android* Phone .Connecting the Intel® Edison board to your Android* Phone with Serial Port Profile (SPP) | Intel® Developer Zone
Let me know if this helps.
I've seen those, but they don't really mention anything about sharing Internet connection.