Final answer:
The phrase in the sentence is the prepositional phrase 'to the elderly lady,' which functions as an adverbial phrase to describe the location of the action.
Step-by-step explanation:
In the sentence 'The nice young man offered his seat to the elderly lady on the bus,' the phrase is the prepositional phrase 'to the elderly lady.' This phrase functions as an adverbial phrase because it describes where the action of offering the seat occurred.
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