You bring up an interesting point. To be honest, as a native English speaker, "there comes a bus" does not sound correct either. Both "HERE comes a bus" and "HERE comes a person" would be preferred. The verb "come" (per its meaning) should not be followed with the preposition "there." Come HERE

I know of "There comes a time..." but not "There comes a bus" ...

I don't see anything grammatically wrong with the sentence....There comes a bus. Having spent a lot of time waiting for busses in my life, I am pretty certain that I have actually used this phrase. The verb "to come" has as one its definitions......to approach. One of the defintions of there.....adv. to that place Here is how it you might use that phrase. You and some other students are waiting at the bus stop for a bus. Any bus would be fine because you are tired of waiting as many busses have already passed by without stopping to pick you up. You see a bus coming to another stop some distance away (there). You say quite naturally, "There comes a bus!" You are not sure if it is your bus, so you don't want to disappoint everyone by saying "Here comes a bus." A bus is arriving "there" but it might not stop for you and your friends. When a bus finally comes to your bus stop then you would say, "Here comes a bus!" "There comes a person." would also be grammatically correct, but you would be more likely to say "There comes somebody."

You can also say 1. "There goes a bus, I have just missed it" or "a bus is coming around the corner" 2." There goes Kaly, she just got on that bus" or "Kaly is coming over to see me, she is coming by bus"