That’s a good start with Hakumen, really; His DDs aren’t really that important to his gameplay - you can use Yukikaze against people who like to do meaty attacks on your wakeup, but Shippu is really only very selectively useful.
At the most basic level, his mixup is 2B or 3C (Okay, if you don’t understand numeric notation, take a moment to go here P4A - How do I read combos…?)) which are both lows, vs 6B, which is an overhead. You can mix in throws, of course, as well. When you’re prepared for more advanced stuff, you start messing around with TK Tsubaki. But fundamentally, mixup in BB is no different from mixup in any game - High/Low/Throw/Frametrap.
You should also try to get an understanding how to apply Hakumen’s drive.
There are basically ~4 components to being good at BB:
#1: Understand the reach, speed and properties of all your attacks and use them appropriately.
#2: Understand how your character moves and the different ways you can approach an opponent, and then use them all to avoid being predictable.
#3: Understand what your mixup/pressure options are, and use them.
#4: Learn combos off bloody everything and be able to confirm into them - at a minimum, you should be able to convert to a combo off a standard ground starter, your overhead, a throw, and an anti-air, plus variants for each of those when your opponent is cornered (or will be pushed to the corner early in the combo). Ideally, you should also have combos for a standard starter on a crouching opponent, a “punish” combo for things like blocked DPs that uses a “big” starter, and a counterhit combo for your basic starter, as well as any character specific stuff (such as combos off counters for Hakumen.)
Also, it might (or might not, dunno) make more sense for this thread to be in the BB section.