B737 Captain reported a bleed valve failure led to having only a single bleed source for pressurization. Due to the flight path involving traversing over the ocean and the pressurization problem; the Captain decided to return to the departure airport.

Narrative

While climbing through 15;000 ft. on our way to ZZZ the left Bleed Trip Off light illuminated. I directed the copilot to run the appropriate checklist; which he did. The light remained on; the pressure gauge confirmed that we had no pneumatic pressure from the left engine. The checklist directed us to open the crossfeed valve so the left side pressure was restored with bleed air from the right engine. The checklist states that icing conditions must be avoided but doesn't otherwise restrict continued flight. However; given that we were tasked with flying more than 2;000 miles across the ocean to arrive at our destination; and continuing to do so would now rely on a single bleed source for pressurization; I had serious reservations about continuing. I transferred control of the airplane to the copilot and contacted Dispatch and Maintenance Control. After discussing the matter with them I decided to return to ZZZ1. Given that we were relying on a single bleed source for pressurization; and would likely be landing significantly over max landing weight; I [requested priority handling]. We asked ATC for a hold to burn fuel and reduce our weight for landing. I used speed brakes; and later extended the gear; to accelerate fuel burn to minimize hold time. After discussion with my copilot I elected to continue holding until we could achieve max landing weight for landing; which we did. I landed the plane normally and we taxied to our assigned gate. I entered a logbook write-up for the left Bleed Trip Off light. Maintenance met us at the gate and we discussed the matter. Scheduling called me and stated that I and my copilot were released from further duty for the remainder of the day and the rest of our trip. I called a Chief Pilot and debriefed him; explaining my decisions to [request priority handling] and return to ZZZ1.