Your example is not a direct message, but a so called "mention" in a channel, which is always visible by everyone else in the same channel.
But you can also send a real direct message to a bot user. It works the same like sending a direct message to any user. e.g. click on the plus next to "Direct Messages", select the bot user from the list and click on go. Now you got a direct messaging channel with that user which is 100% private.
Your bot obviously needs to be ready to receive messages via DM in order to respond correctly. e.g if your are using Slack's Events API you need to subscribe to message.im
to receive posts in the direct message channel to your bot.
Check out this help desk page on how to send direct messages.
Another approach to communicate "secretly" with your bot user in a channel is slash commands, e.g. by posting /mybot hi
in a channel. Both the slash command and respond from your app will not be visible to anyone else in the channel (that is default - but can be changed).