CAPE CANAVERAL, Fla.—An auction for a ride into space next month alongside Jeff Bezos and his brother ended with a winning $28 million bid Saturday. The Amazon founder’s rocket company, Blue Origin, did not disclose the winner’s name following the live online auction. The identity will be revealed in a couple weeks—closer to the brief up-and-down flight from West Texas on July 20, the 52nd anniversary of Neil Armstrong and Buzz Aldrin’s moon landing. It will be the first launch of Blue Origin’s New Shepard rocket with people on board, kicking off the company’s space tourism business. Fifteen previous test flights of the reusable rocket and capsule since 2015—short hops lasting about 10 minutes—were all successful. Saturday’s auction followed more than a month of online bidding that reached $4.8 million by Friday. More than 7,500 people from 159 countries registered to bid, according to Blue Origin. More than 20 bidders—the …