Hi,
I'll ask for some information to try to track down the source of the problem below, but first let's look at how to add a new Bing imagery datasource to your model to see if this helps you with your immediate problem.
To add a new Bing datasource, you choose Add Database Data Source ad you showed in your message. However, you also need to edit the Connection type to be "Bing Maps" rather than "Oracle":

You can change the data source name, as well as the imagery resolution. Once you click OK, you'll have a new, configured Bing datasource:

If you select this datasource and click "Refresh", InfraWorks should try to download new imagery for your model.
Regarding the source of the initial problem, I'm wondering if you might be experiencing problems due to proxy settings. Do you know if your organization uses a proxy server for web access?
One handy way to troubleshoot this issue would be to try to refresh a new Bing datasource added as described above, and check for any warnings or errors written to the InfraWorks log. If you open up the Message Log from the InfraWorks Help menu:

then Refresh the imagery datasource, do you see any errors in the log?
One more thing we can try to troubleshoot is if you can provide the Tracking ID from one of more of the problem models. You can find this in the notification emails sent by InfraWorks:

We can use this ID to look through our logs to see if an error occurred.
I hope this helps,
curt