The Schottky barrier between a metal and a semiconductor plays an important role in determining the transport efficiency of carriers and improving the performance of devices. In this work, we systematically studied the structure and electronic properties of heterostructures of blue phosphorene (BP) in contact with Mo2B based on density functional theory. The semiconductor properties of BP are destroyed owing to strong interaction with bare Mo2B. The effect of modifying Mo2B with O and OH on the contact properties was investigated. A p-type Schottky contact can be obtained in BP/Mo2BO2. The height of the Schottky barrier can be modulated by interlayer distance to realize a transition from a p-type Schottky contact to a p-type Ohmic contact in BP/Mo2BO2. The BP/Mo2B(OH)2 forms robust Ohmic contacts, which are insensitive to interlayer distance and external electric fields due to the Fermi level pinning effect. Our work provides important clues for contact engineering and improvement of device performance based on BP.