You can promote your Apple podcast by adding a widget to your blog's sidebar. In this video, you'll see how to create the widget on your Blogger blog or your self-hosted WordPress blog.
Go to the iTunes Widget Builder to create the widget for your blog. You'll find a pull down button and from there you can choose Podcast Playlist. This will open a dialog box where you can search for the podcasts you want to add to your sidebar. You can see the one I added here on Anchor Boot Camps over on the right (if you are on your desktop computer).
If you are on your mobile device, this link should open in your browser so you can see the widget.
More About iTunes Widget BuilderAt the top of the page on the iTunes Widget Builder, you'll find links to create other cool promotional tools for your blog or any other goodies you have in the iTunes store.
Thanks to Dr. Babe for her callin to my station asking about the podcast widget.