Bird CEO Travis VanderZanden seemed to be making all the right moves recently. His launch of an electric scooter service last year kicked off a larger wave of investment in the sector and spawned clones, as he calls other scooter startups. He already has made a lot of money from Bird, selling shares in the company’s latest $300 million fundraising round, in which it was valued at $2 billion.

But last week, the momentum seemed to shift. Bird’s toughest startup competitor, Lime, announced that Uber and Alphabet had become investors and said that it would sell its scooter rides through the ride-hailing giant’s app. Mr. VanderZanden, in an interview at Bird’s office in Venice, Calif., said Uber approached Bird as well, which hasn’t previously been reported. He said he didn’t like the deal Bird was offered, including the size of the stake Uber wanted and the ride-hailing firm’s desire to put its brand on scooters. Though he didn’t rule out future partnerships with Uber or Lyft, Mr. VanderZanden said he didn’t think getting customers through a ride-hailing app would be an important way to win business.