Bundles

I assume you are referring to the Apple TV app Channels. They are not related to Apple TV+, nor are they bundles.

You sign up for each by starting the subscription in the Apple TV app. The Channels probably have a button like “Try <channel name> free. 7 days free, then $x/month.”

Subscribe to Apple TV channels in the Apple TV app - Apple Support

Apple TV Channels FAQ: Services, pricing, availability, and everything else you need to know - Macworld

The subscriptions as started in the Apple TV app, are exclusive to the Apple TV app. The subscriptions are not exchangeable with subscriptions through separate apps, as there are different perks and different terms & conditions. Some users are better off getting the subscription outside of the Apple TV app, others find more convenience with Apple TV app Channels.

The new Apple TV app and Apple TV app Channels require iOS 12.3 or later.

To get the Showtime / CBS Bundle open the Apple TV App on your Apple TV. Then subscribe to either Showtime or CBS and you will then have both apps for $9.99 mo. I did it this afternoon and it works perfectly.

$9.99 a month for the two (you get both if you click on either to sign up, it appears). More or less a buy one get one free proposition. Obviously it has to be an in-app purchase. I would hope that is the ad free version of CBS. The ad supported version is still available for $6.99

Edit: It seems I was mistaken. Sorry about that. There is a new bundle offer per August 17.

Apple TV+ subscribers get CBS All Access and SHOWTIME bundle at a great value - Apple Newsroom

The press release is a bit thin on how to start this subscription. I am not in a qualifying region, so I can’t check myself. I would expect a special sign-up button for this bundle.

Is the only way to watch the bundled channels inside the app? I can't watch CBS shows in my web browser on my Windows desktop?

Channels I have signed up for I can, but can’t say with these two. Not a current subscriber.