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Sylvia carefully ironed her one good suit to wear to the bank interview
the next day all the while,
Buster, her hairy white cat, waited for her to lay the dark gray
skirt on the bed so that he would have a warm spot to nap.
All the while is an introductory transition. Buster, her hairy white cat, waited for her to lay the dark gray skirt on the bed is a main clause. Generally, you use a comma to connect an introductory transition to the main clause that follows.