BNEP is for Bluetooth BR/EDR (the "classic" bluetooth), not the Bluetooth Low Energy (LE) stack that the RFDuino uses.
There's no reason you couldn't deliver web content (html/css/etc.) through the link provided by the RFduino, but it would require some sort of a gateway service to actually make it available to web browsers --- it would take a moderate amount of effort. RF Digital's newest product, the Simblee, may be an alternative. It supports TCP sockets while connected to a mobile device, so it can easily post to http based web services. (It doesn't natively serve web pages)