An investment group bought Aramark in 2006. Some of the members- J. P. Morgan, Goldman Sachs, Warburg pincus, etc received bailout money from the government in 2008. Would Aramark have gotten any "benefit" or money from that bailout as a private equity holding?
My best understanding is that the acquisition you indicated was completed in 2007, but Aramark retained its identity as a company. TARP was created in 2008, and a comprehensive list of companies that received “bailout” funds can be found at https://projects.propublica.org/bailout/list. I fail to see evidence that Aramark directly received any “bailout” funds.
It is possible that Aramark benefited indirectly if, for example, in the absence of TARP the downturn had been more severe than it actually was and the company went out of business as a result.