For anonymous users to access your Bing maps, they need to be able to access your Bing key without authentication - meaning your Bing key is publicly available. Being that it's publicly available, it is possible for others to obtain your bing maps key and use it in their own applications. Bing maps website has this behavior as well..their Bing key is passed in clear text.
A couple things you can do to prevent usage by other applications (likely similar to procedures employed by Microsoft to prevent unauthorized usage):
1. The link below has instructions for viewing usage. If you see any unexplained usage, change your bing key.
Understanding Bing Maps Transactions
2. Change your bing key regularly. Up to you to determine how necessary this is (maybe check usage every so often and see if it appears anyone has grabbed your key?) From the www.arcgis.com perspective, all maps and hosted apps will be updated by changing the bing key in your organization settings. So you'd only need to make the change in one location. For any apps you've hosted locally, you'd have to check the specific configuration.
Thanks,
Chris
