This paper is deeply motivated by the need to explore the impressive Bitcoin price development by addressing Bitcoin as money in its essential attribute as a medium of exchange. We adopt a monetary economics viewpoint and resort to a representative agent modelling strategy within a money-in-the-utility function (MIUF) framework. First, we show that the impressive Bitcoin price development observed since its inception can be interpreted as a hyperdeflation when we focus on Bitcoin role as a medium of exchange. Second, we show that specific monetary features of Bitcoin, its asymptotical fixed nominal stock and divisibility down to eight decimal places, account for a strong possibility of speculative hyperdeflationary paths. It is shown that those paths are fully consistent with the medium of exchange monetary role of Bitcoin and the representative agent optimizing behavior.