The news comes as Bush is viewed as a potential frontrunner for the Republican nomination for president in 2016. Polls show him running well in key states and many Republicans view him as party's strongest possible nominee.
Campbell said Bush "is still weighing whether or not to pursue the presidency." He has said he plans to make a decision around the end of the year.
Bloomberg reported that Bush teamed with former bankers from Credit Suisse Group AG and Lehman Brothers Holdings Inc. to create a Florida-based investment firm. The firm has made investments tied to the oil and gas industries.
The private equity industry became a focal point in the 2012 campaign. Democrats repeatedly painted Republican nominee Mitt Romney's private equity career in a negative light, in an effort to portray him as out of touch with the concerns of ordinary Americans. If Bush runs for president in 2016, he could face similar attacks.
Updated at 7:14 p.m.