I though about doing this a long time ago but you have a very good start. You know there is a lot easier way of doing this. No gps needed. You just want the bag to stay within a certain distance of the golfer while walking, say 4 ft behind you. You just need a small signal transmitter that could be on a key chain, Then something attached to the arduino that looks at the signal strength to determine distance. Then you just need 2 buttons go and stop so when you actually go to the tee it is not trying to follow you there. That way it works anywhere not just on 1 golf course and if you shank a ball your bag isn't 30ft away from you. Just need a way to identify you from your others in your party. Could even use infrared leds to follow.
Maybe this helps