Today, I was talking to my friend. She is very good at English. During this conversation, she said, "I am on THE bus". I think, she has misused the definite article. In my opinion, it should have been, "I am on A bus". Because this is the first time she said anything about this bus. On the other hand, I know that she generally travel by bus.
You wouldn't normally say on a bus; on the bus is a fixed expression.
The reason why the is used in that phrase is probably because the bus here is something we all know about, something that by extension refers to the institution that represents the (public) transport bus service that uses buses to drive people around the city. The phrase doesn't refer to any bus in particular per se.
In his book, Practical English Usage (69.5), M. Swan says the following:
We use the (with a singular countable noun) when we talk about some kinds of thing that are part of everybody's lives, like ‘the bus’ or ‘the hairdresser’. In this case the bus, for example, does not mean ‘one bus that you know about’; we use the to suggest that taking a bus is a common experience that we all share.
To address the comment and some additional questions one might have after reading the above:
I merely wanted to answer the question of whether on the bus is grammatical in that context, and how that's accomplished – not suggest that on a bus isn't. It would be more usual, given the context the asker provided, for their friend to say I'm on the bus and not I'm on a bus.
I'm on the bus might mean "I'm on the bus I tell you I'm on every day – my school bus", i.e., "...the bus you expect me to be on at this time". It could also mean "I'm on the bus we previously discussed". Et cetera.
Can you say on a bus? Yes, you can say, for example,
I can't talk to you right now, I'm on a bus.
As you said, this introduces a bus; you're talking about it for the first time and identifying the vehicle as a bus.
Last week he was on a bus when an argument erupted between... (independent.co.uk).
He was on a bus – it doesn't matter what bus. The same applies in the example that follows:
"It doesn't. Why would it? I'm nobody." She lowered her chin as her face twisted up. "Just a girl you met on a bus." (Don't Move by Dennis Etchison)
Both are equally acceptable. "On the bus" is usually used in situations where the bus is something the person commonly uses. "On a bus" is used more for one-off type situations.
Why are you so grumpy this morning? Some idiot on the bus kept bothering me.
My parents met on a bus to New York City.
Again, these are not strict rules. Just how they seemed to be used.
Both are correct but express subtle differences.
I'm on the bus. I'll be there in 20 minutes.
Expresses that you are on a specific bus that is meaningful to the conversation. In this case, the assumption is the listener is likely aware of which bus or route you're on so the 20 minute expectation is reasonable.
I'm on a bus. The cell service is really bad.
Expresses that while you are on a bus, it doesn't matter which bus or route, just that your on a bus and that is why you cell service is poor.
If your friend was speaking about how she was travelling at that particular moment in time, then generally in the North of England, 'on the bus' is what one would say. On a bus is not incorrect, because your friend is certainly on a bus, but it is not the usual way to say that one is travelling by bus.
If your friend was not sure that she was on the correct bus for her journey then 'on a bus' would be more appropriate. She is on a bus but it might not be definitely the bus that will get her to where she wants to be.
You could have asked her, "What do you mean you're on the bus? Which one are you on?" And she would have said something like, "Well I'm on the 29 of course, the one I always take to get home."
The definitive article is indeed the one to use here. It's not just any old bus, even though it might actually be a different vehicle, it is one that follows the route she takes every day.