Right now there's not really anything standard out there to get an internet connection over Bluetooth LE, so I'm afraid you would need to build something into your app.
But as far as I know there are no off the shelf implementations available, and even if there were it's pretty insecure to allow any device to access the internet via Bluetooth, which is basically unauthenticated.
Espruino is a JavaScript interpreter for low-power Microcontrollers. This site is both a support community for Espruino and a place to share what you are working on.
Right now there's not really anything standard out there to get an internet connection over Bluetooth LE, so I'm afraid you would need to build something into your app.
There is the HTTP Proxy spec: http://www.espruino.com/BLE+HTTP+Proxy
But as far as I know there are no off the shelf implementations available, and even if there were it's pretty insecure to allow any device to access the internet via Bluetooth, which is basically unauthenticated.