Get name of virtual directory?
Request.ApplicationPath is perfectly reliable way of getting the virtual directory and works always when you have the HttpContext and can ask for the Request data.
For further processing and extracting parts of the path, take a look at the VirtualPathUtility class.
You need to use Request.ApplicationPath. That is what it is designed for.
Editing to go with your comment.
Since you want a 'cleaner' way to handle the slash, I recommend creating a utility function that returns the application path with the logic in it to deal with the slash as you see fit.
Use this function in C#:
public static String GetHost(){ var request = HttpContext.Current.Request; return request.Url.Scheme + "://" + request.ServerVariables["HTTP_HOST"] + request.ApplicationPath;}