The arrival of the wolf in the bachelor's story is important because:
It places Bertha in serious danger and increases the tension in the story.
The bachelor's story gave an altogether different view of the world of imagination. The children started to have keen interest in the bachelor's story as it was different from that of their aunt's.
Bertha was the character in the bachelor's story who was eaten up by the wolf because of the clinging of the medals which she had received because of her good nature.
When Bertha went into the park, she saw pigs and not a single flower in it. This amused the children because for them it was the first story in which the park didn't had flowers but had pigs instead.
The presence of wolf created the sense of tension and increased curiosity among the children. The clinging of the medals paved way for Bertha's death.
The children had heard such a story for the first time. They kept quite and listened silently and patiently to the story.
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