BrightCove Dialogs & Admin UI doesn't load when context path is enabled

[friendlymahi]

Our team uses context path for AEM instances to distinguish our Author and Publisher instances. e.g we access author instance using the Url http://localhost:4502/author

Many ajax calls (especially where servlet/api calls are made), are executed without appending the context path. There are a few occurrences where it is done properly but not across all of them. As a result the ajax call when happens with /bin/brightcove/api instead of /author/bin/brightcove/api and fails since it cant be accessed.