SEATTLE—Fresh off his trip to space, billionaire businessman Jeff Bezos on Monday offered to cover up to $2 billion in NASA costs if the U.S. space agency awards his company Blue Origin a contract to make a spacecraft designed to land astronauts back on the moon. NASA in April awarded rival billionaire entrepreneur Elon Musk’s SpaceX a $2.9 billion contract to build a spacecraft to bring astronauts to the lunar surface as early as 2024, rejecting bids from Blue Origin and defense contractor Dynetics. Blue Origin had partnered with Lockheed Martin Corp, Northrop Grumman Corp, and Draper in the bid. The space agency cited its own funding shortfalls, SpaceX’s proven record of orbital missions, and other factors in a contract decision that senior NASA official Kathy Lueders called “what’s the best value to the government.” In a letter to NASA Administrator Bill Nelson, Bezos said Blue Origin would waive payments …