“I'm riding the bus" or "I'm going by bus" sound the best to me. If you're saying "ride" which means the same thing in this context, you don't need "on" :)

Hi, Paul, that's a great question! The reply can be, "I'm taking the bus." Riding is very specific, because it is related to transportation of a person. Regarding cars and buses, you "ride" them, because you are being supported by the vehicle, so it is giving you a "ride," in other words, "ride" is a way to move you on a physical journey. You can also "ride" a horse or "ride" a bus. You could have said, "I'm riding the bus," but "taking the bus" is the most commonly used colloquial phrase. Remember, if you say, "I'm going," it can only mean you are ABOUT to do something, or you are "going" to do something in the future. This is not the same as already moving in a vehicle - getting a "ride." So you cannot be "going" in your car, your can only be "riding" your car or the bus when it is literally taking you somewhere. I hope this helps! What's the difference between go and ride? Is it possible to say: - I'm going in my car and etc?

I am on the bus.