According to the story, the unfortunate woman in question was left in charge of Bicester House while the house's usual occupants were off fighting for the King during the Civil War.

When the Parliamentary forces closed in on Bicester, the quick-thinking woman gathered up all the valuables she could carry from the house and threw them into a nearby pool known as Rookery Pond.

She presumably hoped that the Parliamentary men would search the house, leave empty-handed and she would be able to reclaim her valuables when the coast was clear. Sadly, the Parliamentary forces, frustrated at not finding the treasures that had hoped to plunder from the house, killed the woman.

The 'White Lady' is said to be seen walking the grounds of the house and the nearby streets on the anniversary of her murder, still searching for her hidden treasure. Even if she was still on the right side of the grave, the woman would struggle to find it as the pond has long since been filled in!

Roger Long's book Curious Oxfordshire also mentions another haunting on the grounds of Bicester House. According to Long there was once a well on the property known as Crock Well. The well was considered dangerous and, after a number of near fatal accidents, was concreted over in the late 19th or early 20th century.

The area around the well is said to be haunted by the figure of a 'Spanish-looking' gentleman who has been seen on a number of occasions, most often by courting couples! Roger Long speculates that this could be the ghost of a Cavalier who is said to have died after falling down the well while fleeing Parliamentary soldiers during the English Civil War.

According to Historic England, only parts of the modern day Bicester House date back to the 17th century as the building was extensively renovated c1780 and again in 1820, so it is likely that the 'Bicester House' of the story refers to a different building on the same site.

I haven't been able to find the location of Crock Well or Rookery Pond, though there is a path known as 'Rookery Way' half a mile to the northwest which may hint at where this pond may have originally been.