What is the meaning of romance at short notice was her specialty in the open window?

The last line, 'Romance at short notice was her specialty' means that she had a quality of creating or making up a story in no time. As we read the story 'The Open Window' we learn that Vera makes up a story about the Open Window, then right after he leaves she makes up a new story about how Mr. Nuttle feared dogs.

Romance here means Creating Stories(Stories that are not true).