Can someone tell me how, or if it's possible, to send street centerline updates to Bing for inclusion in their base maps.
Unless anything has changed in the past couple years, all proposed updates have to be submitted as a feedback/request to Bing.
If you go to https://connect.microsoft.com/bingmaps/Feedback you can propose changes.
You can also go to http://bing.com/maps and in the lower left corner you'll see a link called "Feedback." Click this, and a feedback box will pop up. If you say you want to "make a suggestion" it will refer you to the Microsoft Connect site above. You could, I suppose, report it as a problem (if your proposed change is actually a fix to a problem rather than a suggestion).
It appears that Bing is using basemap data from "Here". They supply mapping information to several big companies and are the backbone of the majority of in-vehicle navigation software. You can become an editor by going to https://mapcreator.here.com or if you're a road authority they have a community partnership agreement that you can pass off data to, but you may have to contact their local office directly.
I don't see a formal way to pass them data but you could use the feedback tool in the bing maps app and they do have a category for missing roads or incorrect roads. Possibly telling them that you will provide data might get you somewhere. I have tried this with google maps in the past and they eventually got to it.