You can use Windows' Scriptable Shell Objects for that. The item object has an ShellFolderItem.ExtendedProperty method

The property you're after is an official Windows property named System.Music.BeatsPerMinute

So, here is how you can use it (you don't need to reference anything, thanks to the cool dynamic C# syntax for COM objects):

static void Main(string[] args)
{
    string path = @"C:\path\kilroy_was_here.mp3";

    // instantiate the Application object
    dynamic shell = Activator.CreateInstance(Type.GetTypeFromProgID("Shell.Application"));

    // get the folder and the child
    var folder = shell.NameSpace(Path.GetDirectoryName(path));
    var item = folder.ParseName(Path.GetFileName(path));

    // get the item's property by it's canonical name. doc says it's a string
    string bpm = item.ExtendedProperty("System.Music.BeatsPerMinute");
    Console.WriteLine(bpm);
}