Vrisharudhamurti is none other than Lord Shiva. Vrishabha, in other words Bull, is the vehicle of Lord Shiva and Lord Shiva being seated on Bull, is called Vrisharidhamurthi. Bull has got many names in association with Lord Shiva, the most popular one is Nandi.
It is in the epics that Vrishabha,i.e, Nandi serves Shiva not only as his vehicles, but also his Gatekeeper.
Whenever Shiva is prepared to out alone, Nandi accompanies him and serves his Master with the highest regards. It is believed that during one of the lighter moments between Lord Shiva and Goddess Parvati, when both of them are involved in a game, Nandi being the Judge, favored his Master, though Shiva was not the winner in that situation.
Furious Parvati had cursed Nandi and said that he would die due to terrible disease. Nandi was excused later and was asked to offer his most liked ones to her son, Lord Ganapati. By this Offering, he could get rid of the curse and could acquire the fame of being one of the best disciples of Lord Shiva.
It was also believed that during the churn of the ocean by divines and demons, when poison came out first as the intermediate resultant, also Nandi had consumed a bit of it, along with Lord Shiva. While Lord Shiva could stop the descent of poison in the throat due to his divine consort, Nandi had gulped in a bit of the dangerous poison and remained alive.
As everyone was surprised, Shiva said that Nandi has got all his powers and his protection. Thus, Vrisharudhamurthi depicts Lord Shiva and Bull together.