Change awaited to awaiting.

Gramatically the sentence is ok. A bus, as a machine, really does not have characteristics like patience. So use of this adverb in this context is portraying a certain style and mood.

There should probably be some commas in there.

Other than that — I think it is crammatically correct, but really clumbsy. Can a bus be patient? there are twoo many ajectives before bus.

I suggest a complete rewrite:

I noticed a blue and white city bus that idled as it awaited the arrival of its passengers.

It’s an awkward sentence.

I noticed that an idling blue and white city bus was patiently awaiting the arrival of its passengers.

I don’t believe the coma is necessary between idling and blue as idling was one of the things the bus was doing.