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.