I also have a 2011 S. Nothing is bluetoothed on it. The little OBDI-looking port under the "gas tank" is where you could connect a laptop computer and talk to the motorcycle's computer.
Before you spend a lot of time and money ordering random parts online, I recommend narrowing down exactly what's gone wrong.
The throttle is simply a 5K potentiometer with 2 wires coming off. The hardest part about checking it is connecting your multimeter to the tiny plugs. I just shoved two needles through the plastic of the two wires, then alligator-clipped the multimeter to the needles. If that doesn't give you a range of roughly 0K to 5K, then the throttle is bad. Not likely, but possible. I have three throttles at my house. None of them is bad except the one that I bought, new, online.
The place where I was having throttle problems is under the "gas tank" where the throttle plugs in to some other wires. There's a lose connection somewhere and whenever those wires would shift and move to port, then I would lose all throttle response. My solution was to zip-time them all tight towards the starboard side and I never had a problem since.
Assuming throttle and connection are good, then I would look at the motor-controller. It's on the far-bottom of your motorcycle. These Alltrax controllers DO go bad sometimes. (Mine went bad while the motorcycle was still under warranty and Zero replaced it for free.) Make sure your throttle wires are attached to the controller and a mouse didn't unplug one. Or that you didn't accidentally plug stuff up wrong when you were trying to access the battery. There's an LED on the controller that can tell you if it's passing or failing at bootup and can blink an error code, but the geniuses at Zero thought it would be hilarious to hide that controller under your motorcycle so that you can't really see the LED and use it as intended.
Check those things first, as they are more-likely failure points and easier to check. Let me know what you find out so we'll know where to focus, using my Zero as a reference.
This will be a lot easier than getting the battery out of the Zero was.