*Catching a bus* describes the process of getting to a stop/station, waiting and boarding.

*Taking a bus* describes the entire process, including the journey itself.

Much of the time, the distinction isn't important. For example:

> "How did you get to work today?"

> "I caught a bus." *(The listener infers that having caught the bus, you stay on it)*

> "I took the bus." *(You have described the journey)*

However, it could be relevant:

> "I read a book while I was taking the bus" *(yes: reading while the bus is moving)*

> "I read a book while I was catching the bus" *(unlikely: reading while stepping onto the bus, paying the driver, etc.)*

It is a similar meaning to *catch* as catching a fish, or catching a ball. You and the bus are apart, and then you bring yourself into contact with it through your own effort.