B737-700 First Officer reported loss of B Hydraulic System Fluid Quantity. The flight crew turned off the Hydraulic Pumps and requested priority handling. A precautionary landing was made at destination airport.

Narrative

During climbout of ZZZ1; we noticed that Hydraulic System B quantity started to bleed below required levels and continued to bleed to zero. We noticed the ENG 2 hydraulic pump LOW PRESSURE light illuminate. The Captain proceeded to perform the Quick Reference Handbook for a Hydraulic Pump LOW PRESSURE (B SYS). After some time; we noticed that the Hydraulic Pressure started to bleed pressure to zero and the ELEC 1 hydraulic pump LOW PRESSURE light illuminated. The Captain then proceeded to perform the loss of hydraulic system B Quick Reference Handbook. The Captain and I saw that hydraulic system A was still operating and was confident that we can make it back to ZZZ2 but also made contingency plans if it did fail enroute. We requested priority handling when we got on with ZZZ2 Center and safely landed in ZZZ2.Lessons learned was to continue to work as a crew and communication between flight crew is critical. The Captain and I went through multiple plans and discussed other possible errors and threats. Training proved to be of extreme help due to the scenarios we went through.