They are professional drivers, so you can rely on them being better than the average drivers in difficult situations like having to brake suddenly, so I think you should cut them off preferentially.
Same reason why a bus will not suddenly slow down to let you into their lane unless lives are at stake. Which at sub 30mph speeds they're not.
Best to treat a city bus like it's a train.
You can think of being a bus driver in city traffic as a constant trolley problem. As a professional driver, do you risk injuring 50 people inside the bus or 1 idiot on the road?
Busses are big and may not stop quickly. If traffic is tight enough that I need to force my way into an opening, traffic may stop suddenly and I don't want to find out if the bus can stop behind me, because if not, I need to shop for a new car and new pants. If things are moving very slowly, then yeah, you can cut them off.
This is going to be a major challenge or at least a major change for Waymo. It's been a while since I've driven near one, but they were very timid with lane changes. Also, there was that published incident when the Waymo car tried to change lanes into a bus.
There's unwritten rules about who you can cut off. My experience is from LA freeways, the rules may be different in NYC, but the concept is the same. Buses and other vehicles, usually no, but sometimes. Marked taxis, no. Older vehicle with lots of scrapes, probably no. Also, the proper time to signal your lane change is often after your car is already in the lane enough that you can't be displaced.