Can you play the PS4 Black Ops 4 offline? Yes you can & you will have to play against or with bots but you can play both the maps and the zombies or customize your own game. You wont be able to rank up and Prestige in both the Multiplayer and Zombies side but you can still have fun and learn the maps or games.

You'll want to go to "Private Match" (which you can play alone or with friends, including split-screen co-op if you'd like to play with a local friend or family). You can play any of the modes here, but if you want bots, you'll need to go to Game Settings < Bots, then configure as you wish.