I don't think it is possible to obtain the link to a specific episode, either from the iTunes app on iOS where you can browse the store, or from the iOS music app after if has already been downloaded.
Often a direct link to the episode is included in the show notes that are included, but the built in apps have scant support for allowing you to actually view these properly, they just overlay the text (or the top section of it) without giving you a way to interact with it.
To be honest, and I know you specifically asked not to suggest other apps, but given the above should hopefully be a suitable answer in it's own right I will do so anyway. Try Instacast, it's a far superior app for both downloading/subscribing and actually listening to podcasts. As you can see if allows full acces to the show notes, you can just click the download link provided to copy the URL, or use the built in sharing functions.
While you are at it, you should download the Ask Different Podcast to test it ;)