Bain Capital is the third company to exit the consortium, after the departures of Kohlberg Kravis Roberts (KKR) and CVC earlier this week amidst concerns about the performance of some of Coles' businesses.
The exit of Bain Capital leaves three private equity companies - Carlyle Group, Texas Pacific Group and Blackstone - still in the consortium.
However, Wesfarmers - one of Australia's largest public companies - has offered Aus$19.7 billion (£8.25 billion) for Coles. And there is speculation that main rival, Woolworths - Australia's largest retailer - is also in talks about joining a possible bid for Coles valued at more than Aus$20 billion (£8.37 billion).
Coles put itself up for sale in February after a profit downgrade, following declining sales in its supermarket division.