<p>Uncertainty minimization is an important feature of any decision-making and transportation problem. Uncertainty and imprecisions in day-to-day life is very well tackled by decision making methods. A number of studies has been done to modelling uncertainty for fuzzy, intuitionistic fuzzy and hesitant fuzzy information. The existing methods of uncertainty modelling have some important shortcomings and limitations. To deal with these limitations, we have adopted the notion of hesitant bifuzzy set (HBFS), as an extension dual hesitant fuzzy set for its ability to deal with uncertainty and ambiguity without any restrictions. In this article we have developed a series of novel score functions for hesitant bifuzzy elements and HBFS. We have also developed a model for hesitant bifuzzy transportation problem to show the applicability of developed score function. Generalized hesitant bi-fuzzy modified distribution method has also been developed to find the optimal solution of defined hesitant bifuzzy transportation problem. To illustrate the developed method, an illustrative example of COVID-19 Vaccine transportation problem is taken. A sensitive analysis has also been conducted to distinguish different cost through different score functions. To show the outperformance of developed method, a comparative study has been carried out with the pre-existing methods.</p>