The word "dancing" is being used as a participle in the sentence: "We were distracted by the bear as it was dancing."
In this sentence, "dancing" describes what the bear is doing, functioning as a verb form that acts as part of the verb phrase.
In the other sentences:
- "The dancing bear was part of the circus act": Here, "dancing" is an adjective describing the bear.
- "Dancing is unusual for a bear": In this case, "dancing" functions as a noun.
So, the correct answer is just the first sentence.