I wondered, why is it that on some buses there are conductors that sell bus riders tickets whereas on some other buses there are none?
There are diferent kinds of city buses. The new ones have auto-pay systems. Most local residents buy "IC" cards. They swipe their cards as they get on and off the buses. There are still conductors on these buses, whose main duty is to make sure people would use their cards.
Some old buses, mostly shorter ones, have a dropbox at the door next the driver. Passengers drop their money in the box, commonly one yuan, as they board the bus. They get off using the rear exist. There do not seem to be conductors on these buses. You better carry small bills or coins to go on these buses.
Bus fares also differ. For example, in Beijing, charges on buses labelled 2xx and below are uniformly one yuan, regardless where you board and get off. Buses labelled 300 up to 599 charge by distance - it is like one yuan for first 10 km; you pay a little more for each additional km. 600 and above buses seem to have different charging scales for themselves. Really traveling by buses in Chinese cities is cheap. The only issue is that they're often too crowded, especially during rush hours.