All games played against Bots or the Coach on web and mobile are automatically saved to your Game History when the match ends, as long as the minimum ply requirement is met:

These saved games are only visible to you. You can find them in your Game History on the homepage (if enabled) and on your profile. To view only Bot or Coach games, use the tabs at the top of the Game History page.

If your Bot or Coach game is shorter than the required number of ply, you can save it manually. On web, click 'Save to Archive.' On mobile, tap 'Options' and then 'Save Game.'

To delete a bot game, open it from your archive and click the trash can icon ('Delete Game') at the bottom of the right sidebar:

To delete a bot game on the Chess.com app for iOS or Android, tap 'Options' in the bottom menu, then select 'Delete Game.'