It usually takes me a few seconds to get across an intersection, although it would depend a bit on whether I have a rolling start, or had stopped for the light.
It sounds like the bus may have done a right turn on red which is typically legal if there is no traffic. If it was a right turn on a stale yellow, the bike rider should have seen it and held back a bit.
It is not uncommon for drivers to ignore the existence of bicycles on a shoulder as part of traffic patterns.
Nonetheless, one should always aware that buses, trucks, and large vehicles cut corners on the inside, and swing wide, and they should be given a little extra space. And, the drivers, of course, should be aware of that too.