Air carrier pilot reported an ENG (Engine) bleed air fault on take off. Flight crew followed procedures and returned to the departure airport.

Narrative

Shortly after climbing through 10k experienced AIR ENG (Engine) 2 Bleed fault. Ran proper procedures; but we could not continue with an inoperative ENG 2 bleed.Return to Base (RTB) back to ZZZ landing safely without incident.All icing conditions were avoided out of precaution for Eng 2 bleed inoperative condition.Overweight landing was not accomplished; did not need to declare an emergency.Taxi back to the gate for tail swap to continue on with scheduled ZZZ- ZZZ1 flight.