How much would you pay to know that you could see your doctor almost any time you choose, that your appointment would begin on time, and that if you had questions later, you could send an email and get a response?

1Life Healthcare Inc.--a start-up whose backers include Benchmark Capital, DAG Ventures and Oak Investment Partners--is betting it's $199 per year. That's what it charges for a service that enables patients to schedule physician appointments at its centers almost any time, including weekends, and to be able to email...