BST will attach some where (I always place a twig/branch in the container for them). If you can get to see them make the chrysalis it is a very cool process!
It is not advisable to go give them store bought dill or parsley or plants bought at box stores. There can be chemicals on it that will kill them. Use what you have in your garden. Host plants for BST are dill, parsley, & fennel. I have grown Bronze fennel for years for them to lay there eggs on.