To root original BlueStacks vm you can use BlueStacks MultiTool. But I have more simpler solution. You can just download already rooted BlueStacks image.
There are two version of rooted BlueStacks available for download:
- BlueStacks Rooted setup v0.8.12.3119 Mod – android 4.0.4 (recomended, more stable!!!)
- BlueStacks Rooted Superuser setup v0.9.3.4070 Mod – android 4.4.2
Remove your old BlueStacks and install rooted vm.