Most of this is just my personal oppinions, so here goes. Why I think that it's better to bike than use a Bus.
1 - My commute is 9km, relatively short, with a Bike I get to the office faster than I would if I used a bus.
2 - No running to the bust stop when you see the bus comming.
3 - No waiting for the bus to get there
4 - No need to hunt for a place to sit
5 - No annoying people right up there in my personal space.
6 - It's still healthier to ride a bike than take the bus.
The only advantages I see the bus has over a bike are:
1 - Weather protection
2 - Long range and quick when using express buses.
I'll take a bike instead.