"Romance at short notice was her speciality." Justify this observation about Vera.

The term "romance" is usually associated with love stories, but the definition of the word, according to the Merriam-Webster online dictionary includes these meanings:


a (1) :  a medieval tale based on legend, chivalric love and adventure, or the supernatural (2) : a prose narrative treating imaginary characters involved in events remote in time or place and usually heroic, adventurous, or mysterious 


2:  something (as an extravagant story or account) that lacks basis in fact

When the narrator of "The Open Window" says that "Romance at short notice was her specialty" it means that Vera was adept in making up "extravagant" stories full of mysterious events. No doubt Vera likes that kind of reading material herself. H. Ryder Haggard's popular Victorian novels would be good examples. Vera is obviously bored with her confinement in an English country manor and must be indulging in escapism in her reading as well as in her own imagination. 
 
Vera invents two stories on the spur of the moment. One she tells her visitor Framton Nuttel when they first meet. She only has a few minutes before her aunt will appear and take over as hostess. During that time Vera tells Nuttel how her aunt's husband and two brothers were sucked into a bog three years ago and never seen again. Her story sets Framton up to believe he is seeing ghosts when the three men appear outside headed towards the open window. Then at the end Vera invents another lurid story to explain Framton Nuttel's sudden disappearance.


"A most extraordinary man, a Mr. Nuttel," said Mrs. Sappleton; "could only talk about his illnesses, and dashed off without a word of goodby or apology when you arrived. One would think he had seen a ghost."
"I expect it was the spaniel," said the niece calmly; "he told me he had a horror of dogs. He was once hunted into a cemetery somewhere on the banks of the Ganges by a pack of pariah dogs, and had to spend the night in a newly dug grave with the creatures snarling and grinning and foaming just above him. Enough to make anyone lose their nerve."

Vera is an exceptionally intelligent and creative girl. Yet she must have gotten some help from her reading when she invented the story about a man being hunted by a pack of pariah dogs and spending the night in a newly dug grave.