Coherence in sentence (2)
"After all other people had already boarded the bus, the bus conductor came to the hotel cafeteria and warned us to hurry up, or we would have to get to the airport BY OUR OWN MEANS."
is correct, but
"After all other people had already boarded the bus, the bus conductor came to the hotel cafeteria and warned us to hurry up, or we would have to get to the airport ON OUR OWN."
would also sound good.
"BY OUR OWN MEANS" indicates that if you didn't hurry up, you would have to go to the airport using another method/way of transportation and not that particular bus. It basically means that you'd have to go to the airport "ON YOUR OWN" some way or the other.