The Battle Edition, usually $40, contains both the Blackout battle royale mode and multiplayer, but not the Zombies mode.
As a reminder, a subscription to the Humble Monthly Bundle costs $12 a month, but you can cancel it at anytime. If you wanted, you could just grab Black Ops 4 and then cancel before the next bundle. You'd get access to the Battle Edition plus all of the other games in June's bundle, the full contents of which will be announced at the start of next month.
You can also pause your subscription at any time, stopping the money leaving your account if you don't like the look of an upcoming bundle. You can then reactivate it when you see a bundle you fancy.
You can check out Steven's review of Black Ops 4 here—just discount the zombie bits.
You can activate your subscription here.