This question can be easily answered in two parts.
First, white is typically the color used to represent innocence or purity. In this case, Jewett is referring to sexual purity.
Secondly, birds often represent freedom, and the ability to move from place to place on one's whim.
When you combine these two common symbols, you get an uncommon suggestion that women can maintain freedom and purity. The bird is a paradox, a seeming contradiction, and Jewett wants you to consider that contradiction and all its implications.
What does the story, now that you understand this symbol, now reveal about womens' liberation?