Learn Spanish (Spain): Esperamos a la jefa en el restaurante. - We are waiting for the boss in the restaurant.

Yes, esperar means 'to wait for', so you do not need a separate word to translate 'for'. However, the a here is the 'personal a'. In Spanish, when the direct object of an action is a specific person (like la jefa), you must put an a right before them.

If I wanted to say 'We are waiting for the bus', would I still use the 'a'?

No. The personal a is only used for people (and sometimes beloved pets). Because a bus is an object, you would just say Esperamos el autobús without the a.

Does esperar always mean 'to wait'?

It can mean 'to wait', 'to hope', or 'to expect'. In this sentence, because they are at a restaurant waiting for someone to arrive, 'to wait' is the most logical translation.

I learned that 'boss' is el jefe. Why does this sentence use la jefa?

Like many Spanish nouns referring to people, jefe changes to match the person's gender. Since the boss they are waiting for in this sentence is a woman, the word changes to the feminine form, la jefa.