Hello,
we have read your project description and after a brief discussion between our employes, we propose you a possible solution.
Web server is required, If your plan is to have your own login/register system connected with a database of users; the facebook/twitter login can be done easily by using their API.
Your idea of using bluetooth is suitable, although it could be very inconsistent in terms of the distance and walls between the users, and there are also some problems with the bluetooth after iOS 7 update. There is a possibility for a pure p2p connection with the iOS 7 update, but the module is still not reliable and consistent.
The best option in our opinion is to have separate server(web server) which will handle the HTTP requests and the phone GPS coordinates can be used for determining the distance. The only downside is the internet requirement, but nowadays almost all of the iPhone/iPad users have internet connection.
The development of the app would take approximately 20 days and the work process will be done by following the rules of the SCRUM agile framework. Looking forward to speak with you about the details of the project.
Best Regards!