If you go to Bing.com you can see your information in the upper right (right above the picture). When you get enough points, you can click your name at Bing.com and click Redeem. Then you can choose a Windows Phone 8 gift card. You'll get an email with a code, then you add that as a Microsoft gift card in the Wallet app.
I doubt there is anyway to do most of that in any app, you'll probably have to use a web browser