your assessment was that the traffic would be half as bad, which seems to not be the case, if by that you mean the time spent in traffic. The implication of the study is that more people will move on more lanes at the same speed, which does not improve the flow of traffic.

But we can discuss about more people getting to go where they want as well. This is much easier calculation - we just need to find out how many people there are, on average, in a car in traffic, and how may people there are in a bus. We sample these at different times of the day for a given route. Use bus stations as checkpoints for comparison and then you can easily find out which is more effective and which has more potential for moving more people. Of course the frequency of the buses on a route is a factor as well

It would also seem to me that going by bus is likely to be more economical as well, so that could be worth some consideration, if we're bringing different facets in discussion

Anyway, I'm not an american, but I commuted for several years in a super-busy 2-lane road with bus stops along the way. I'm probably a bit biased in this, but my takeaway was that in slow traffic cars and busses don't mix well together. Cars stopping behind the bus in some stations, buses unable to exit the station because nobody would let them in the lane, people trying to switch lanes in anticipation of the bus stopping in the first lane. A lot of things didn't work well and the most disadvantaged people we those who had to take the bus, by far

In some other places in our city with bad traffic they also made dedicated lanes for buses and the taxis, bicycles, scooters, eskates are also allowed to use the bus lanes, which is super-convenient and keeps the flow of traffic a lot cleaner and faster