There is an interesting story mentioned in The Skanda Purana where this Vrta is prescribed to a Bhramin lady.
Once a Brahmin lady came to Sandilya Muni with two boys, her son, Suchivrata, and an orphan prince, Dharmagupta, whose father was killed in battle and the kingdom was taken over by enemies. Acting upon the advice of Sandilya Muni, the woman and the boys performed the Vrata with great devotion. After four months, that is, in the eighth Pradosha, Suchivrata obtained a pot of nectar and drank the divine Amruta. Prince Dharmagupta won the hand of a celestial princess and, as ordered by Lord Siva, with the help of the celestial king himself, his enemies were slain and his kingdom restored to him. Then Dharmagupta attained the Lord’s supreme abode.
A very important point to be remembered in this connection is that during this auspicious period all the hosts of celestial beings and gods come down from the heavens and attend the worship in their subtle forms. This adds immensely to the sanctity of the worship.
The mere sight of the Deity in a temple during this period will destroy all sins, and bestow bountiful blessings and Grace upon the fortunate beholder. Even a single bel leaf offered to the Lord at this unique, auspicious moment equals a hundred Mahapujas. The importance of offering Bilva to Shiva is stated in Bilva Ashtakam:
“Tridalam Trigunakaaram Trinethram Cha Triyayusham,
Trijanma Papa Samharam Eka Bilwam Shivarpanam”
I offer one leaf of Bilwa to Lord Shiva,
Which has three leaves,
causes three qualities,
that is like the three eyes of Shiva,
Which is like the triad of weapons,
And which destroys the sins of three births.
Origin of the Vrta
The Vrta is said to be originated during the Samudra Manthan, as mentioned in Shiva Purana, it all began with the churning of the milk ocean by the Gods and the Demons on a holy Dwadasi day. While they were churning the Ocean with Vasuki being the Rope. Lord Vishnu held Mount Meru which was used as a churner in his Kurma Avatar, the tortoise incarnation. The first item that came up was Hala Hal, the most deadly poison, that was capable of destroying the whole universe. The poison sent dreadful shivers amongst every entity in the universe.