In 2002 Andrews, Lewis and Lovejoy introduced partition function PD(n), the number of partitions of n with designated summands and using modular forms they obtained many congruences modulo 3 and powers of 2. For example, they proved \(PD(3n+2)\equiv 0 \pmod {3}\). In this paper, we study various arithmetic properties of \(PD_2(n)\) modulo 3 and powers of 2, where \(PD_2(n)\) denotes the number of bipartitions of n with designated summands. We obtain congruences like \(PD_2(3^{\alpha +3}(3n+2))\equiv 0 \pmod {3}\), \(PD_2(3^{\alpha +3}(6n+4))\equiv 0 \pmod {3}\), \(PD_2(24n+15)\equiv 0\pmod {2^5}\), \(PD_2(24n+23)\equiv 0\pmod {2^5}\), \(PD_2(24n+12)\equiv 0\pmod {12}\) and \(PD_2(18n+15)\equiv 0\pmod {48}\).