Okay, now I understand your needs. I am currently working on OSMDroid version 6.1.14 which has support for displaying Bing maps, also HEREWEGo maps, MapQuest, MapBox, Thunderforest etc. If that would help you, I can send you the BETA version of the library.
WebView is not a standard browser like Firefox or Chrome and it is very difficult to get the results you want. Changing UserAgent to WebView causes more problems than good, so it's not really the best option.