There is no direct connection from Amritsar to Bhākra. However, you can take the train to Phagwara Junction (PGW) then take the taxi to Bhākra. Alternatively, you can travel from Amritsar to Bhākra in around 2 h 37 min.
From Amritsar Junction (ASR) train to Phagwara Junction (PGW) then taxi to Bhākra. 3 h 29 min ₹2,729. From Amritsar taxi to Bhākra. 2 h 37 min ₹5,828. From Amritsar drive to Bhākra. 2 h 37 min ₹1,405.