BOSTON—The head of a private equity firm and former Staples Inc. executive convicted of bribery and fraud charges for trying to pay more than $1.2 million to buy his three children’s way into elite universities asked the court Friday to allow him to remain free pending his appeal. John Wilson, 62, was sentenced last month to 15 months in prison, the longest sentence so far handed down in the sprawling college admissions bribery scandal dubbed Operation Varsity Blues that ensnared nearly 60 parents as well as college athletic officials. Wilson was accused of paying $220,000 to have his son designated as a University of Southern California water polo recruit, and $1 million to buy his twin daughters’ ways into Harvard and Stanford, and then filing a false tax return claiming part of it as a tax write-off. His attorneys in their motion Friday made several arguments: the prosecution’s legal theories …