I'm also working on a scouting app using bluetooth.
Here's a good blog post explaining how to connect an android device to a computer, using JR-82 and bluetooth. I haven't tried it yet, but it looks like it will work alright.
The network design I'm planning on implementing would be completely decentralized, able to sync data across devices in the pit without internet access automatically, and completely network fault tolerant, not being tied to a laptop in the stands.
To address OP's question though, I don't think 2-3 months is quite enough time to learn how to do mobile app development. Last year, I implemented a system that relied on manually copying data to and from a central laptop over a USB cord with windows explorer. It was pretty ghetto, but it worked pretty well. You can see the source for the desktop version
here, and the android version can be downloaded
here. Let me know if you want me to put the source for that up. This is what I managed to make in about 3 months on my own with experience with Java. I'm not saying that to brag at all though, I'm not very happy with how the app turned out, and alot of the code inside is absolutely horrible because I was very rushed with mid competition bug-fixes.
All that being said, I thought it was a great experience, and I learned a lot by doing it, and you should definitely give it a shot, whatever method you choose. Just make sure you have a good backup solution like paper or another app, like I did, for if your app isn't ready in time. You can always take what you've made and polish it up in the off season for next year.