Shares in Aberdeen-based FirstGroup, which has a market value of about 1.34 billion pounds ($1.81 billion), fell more than 10 percent on the news. They were down 7.5 percent at 103 pence at 0840 GMT.
In April, it said it had turned down a “possible cash offer” from the U.S. fund, raising concerns among investors that it could be forced to break itself up or sell off parts of its business.
Apollo, which under British rules had until May 9 to take a decision, has now said it is walking away from the business, which operates Greyhound intercity coaches and school buses in North America and rail services in the UK.
Apollo declined to give further details on the decision when asked by Reuters.
FirstGroup’s shares have slumped since the middle of last year and were hit again by a profit warning which saw them drop to 77 pence in March, their lowest since the company listed in 1995.
FirstGroup has also been targeted by Canadian activist investor West Face Capital, which disclosed a 5 percent stake in the business last June.
Reporting by Clara Denina, editing by Louise Heavens