From the showcase mobile app on iPhone (with iOS7 on iPhone 4 this works fine).
choose Fetch Contact example, click on Fetch Contact button, select contact (if already have bridgeIt, if not get bridgeIt first then select contact).
as soon as contact is selected the screen will exit bridgeIt but not return to Safari, see attached screen shot. Even if you go back into Safari and the web app and press upload, the contact is not uploaded.

Further debugging indicates that the BridgeIt iOS app. is closing to the home screen immediately following the user selection of a contact. This seems to be related to the "Contacts" permissions settings on the phone. In some cases, users who download the bridgeit app. and respond to the security popup the first time that the Fetch Contact demo is run with "Always Allow" will have the "Contacts" settings added and enabled in the BridgeIt Settings under "Allow BridgeIt to Access:". In these cases (when the setting is added), the app. works as expected and returns a contact to the web application. However, in many cases the the app. will instead crash to the home screen, and there will be no entry for "Contacts" in the BridgeIt Settings screen.

This crash can also be reproduced by disabling access to the "Contacts" in the BridgeIt Settings screen.

So this issue is somehow related to the access restrictions code in the BridgeIt app.