Bipolarity plays a key role in different domains such as technology, social networking and biological sciences for illustrating real-world phenomenon using bipolar fuzzy models. In this article, novel concepts of bipolar fuzzy competition hypergraphs are introduced and discuss the application of the proposed model. The main contribution is to illustrate different methods for the construction of bipolar fuzzy competition hypergraphs and their variants. Authors study various new concepts including bipolar fuzzy row hypergraphs, bipolar fuzzy column hypergraphs, bipolar fuzzy k-competition hypergraphs, bipolar fuzzy neighborhood hypergraphs and strong hyperedges. Besides, we develop some relations between bipolar fuzzy k-competition hypergraphs and bipolar fuzzy neighborhood hypergraphs. Moreover, authors design an algorithm to compute the strength of competition among companies in business market. A comparative analysis of the proposed model is discuss with the existing models such bipolar fuzzy competition graphs and fuzzy competition hypergraphs.