What road is this on?

I strongly advise avoiding the narrow two way streets, on which there are often buses in both directions. An example is Gates Avenue. Parking both sides, buses both sides, and narrow lanes. No thanks! I'd rather go a few blocks north and take Dekalb. One way with a bike lane, too! Much more sane.

The best thing you can do to keep yourself safe riding in NYC is to choose your routes carefully. If you find yourself on a road that feels unsafe, there is almost always a better choice within a few blocks. The most direct route is almost never the best one, and you may find that less direct but safer routes can be faster because you can ride more confidently. Plan before you go, and if you find you planned wrong, don't be afraid to change.

If they are in front of me, and stop at a bus stop. I ride around them.

A very close call today for me. A bus sped past me with perhaps just an inch from me (at least that's how I felt). There was a sizable truck on the left lane, and this bus driver, instead of waiting for a few seconds when the truck and me were not side by side, squeezed through between me and the truck in high speed. I was a little shaken as it passed because it had a long body, so I had to make sure to maintain perfect balance... For thought after it passed: glad to be alive for Christmas.

Wanted to read its license number but it continued to go fast. Maybe the driver has something urgent waiting for him?

Was it a regional transportation bus, school bus, or a bus used by a church or retirement home? If it was a regional transportation bus. All you need to do is call the regional transportation service(usually part of the city/county government) and tell them the route #, direction, and time of day, to locate the driver. Of course include what happened. If the bus belonged to a church, retirement home, or some disability services organization. Call the church/retirement home/disability services organization. They will be easier to find. Because they don't have route #'s.

Thanks. It seemed to be an express bus, could be off-duty, though, since I don't remember ever encoutering them there before.

An addendum:

In terms of a regional transit bus. If you don't use a mirror, which would give you the chance to see the destination listed, since they were going the same direction. All you would have to do is remember the route number from the back of the bus. The direction you were traveling(ex. south on Lombard St. in San Francisco), at the time, and the general time of day.

Since you think it would be an express bus. That would mean during AM or PM-Rush. If it was an 'off-duty' regional transit bus. It would say 'Not In Service', on the electronic sign on the front. Also, The express busses will generally take different routes than the regular routes. They may use the local interstate on a consistent basis.

Was it the shape of a:

regional transit bus: long, rectangular, no curved edges on top

School bus: long, curved edges on top, some with engine in front of driver, some with engine underneath driver; short, curved edges on top, engine in front of driver

Church/DSS bus: short, curved edges on top, engine in front of driver

I have two mirrors. Though I check the mirrors often, it's impossible to look at them all the time, and I was riding to the far right side of the street, all other vehicles passed me in reasonable distance. I didn't expect the appearance of this bus, as it's very fast. Even if I saw it, I had nowhere to go, since to my right were parked cars. Really, if I had leaned just a tiny bit to the left while it's passing, I might not be posting here today. The bus looked like the one in the following picture, but I didn't get any numbers on it:
https://upload.wikimedia.org/wikiped...%282007%29.jpg

Ah, yes. There is a bus locally like that. Which goes from one local metro transit station(13mi. outside the center of Washington, DC). To BWI-Thurgood Marshall Airport, in Baltimore. It is run by the state transportation association. Greyhound, Trailways, Peter Pan, etc., use that kind of bus. Charter companies also use that kind of bus.

Type in "Bicycle accident & bus" in Google and start reading all the horror stories. As a daily bus rider, you do not want to play leap frog with the bus. The driver is distracted by passengers boarding and unboarding the bus. He's also controlling the fare box handing out transfers and opening the back door. Did I tell you that most morning bus drivers have to wake up between 4-5 in the morning?

If you can't pass the bus, stop for 5 minutes (or less) and let him go. I sat in the driver's seat once and there are many blind spots. Don't depend on the driver seeing you because if he make a mistake, you will pay for it.