I'll be interested to see how this works from afar in New York. To my mind it's likely to just make for more traffic and not take a sizable number of cars off the road, but I'd love to be proven wrong.
A bus takes up the space of 3-4 cars. If there are more than 4 people on the bus, it is increasing the capacity of the road. Surely there are some negative effects because busses stop & take longer to turn, but I also don't think their business plan involves driving busses with only 4 people on them.
I have a fifteen minute walk to work. If there was a convenient bus that cut that in half, I would use it. I used to ride the subway to work. That took about 40 minutes. I would definitely consider using a bus instead if the circumstances were right.
AFAICT most people who drive to work in Manhattan on a regular basis do so because they live far enough out in the boroughs or suburbs that getting to the subway/commuter rail is a PITA.
There is a large contingent in residential areas of Manhattan above 59th St. that take cabs to work -- especially on the East Side where the subway is often too crowded to get on. Although the 2nd Ave subway (if it opens as projected in 2017) will probably make the subway a more palatable option, I could see something like this being an alternative for some of those riders -- cabs can be difficult to find in the morning, and this would be far less expensive.
This often comes up in the context of building more roads to alleviate congestion. It won't work, the theory goes, because when congestion reduces more people start driving, until the congestion reaches equilibrium again.
If buses take cars off the street and reduce congestion, the same argument applies; emergent demand will mean any cars taken off the street will soon be replaced.
Personally emergent demand has always struck me as a rather defeatist idea :)
While this sounds plausible, it doesn't follow that building roads or adding buses is a bad idea. Even if the congestion stays constant, now more people get to travel.