One of those links provided by a commenter led me to another link
here , from which I ended up wit this, which works:
HttpClient http = new HttpClient();
String httpqry = String.Format("http://dev.virtualearth.net/REST/v1/Locations/{0},{1}?o=xml&key={2}", location.Latitude.ToString(), location.Longitude.ToString(), App.BingMapsKey);
HttpResponseMessage resp = await http.GetAsync(httpqry);
resp.EnsureSuccessStatusCode();
Stream strom = await resp.Content.ReadAsStreamAsync();
XDocument xdoc = XDocument.Load(strom);
XNamespace bmn = App.BingMapsNamespace;
String addressLine = (from l in xdoc.Descendants(bmn + "Address") select l).First().Value;
String municipality = (from l in xdoc.Descendants(bmn + "Locality") select l).First().Value;
String stateProv = (from l in xdoc.Descendants(bmn + "AdminDistrict") select l).First().Value;
String postalCode = (from l in xdoc.Descendants(bmn + "PostalCode") select l).First().Value;
String country = (from l in xdoc.Descendants(bmn + "CountryRegion") select l).First().Value;
How the new URL differs from the old, I can't tell - maybe it's in how it's built, or...? At any rate, it works, so I'm happy and will move on to the next challenge.