Hayden Wood stayed on at the bust supplier on a £250,000 salary after it collapsed last autumn and was propped up by the taxpayer.
Bulb said Hayden Wood was “stepping back from the business”.
“We wish him all the best for the future,” it added.
He will not be replaced, with the role being split among the remining executive team.
Mr Wood stayed on at Bulb after it was placed into a “special administration” when it collapsed in November last year and was propped up with an initial taxpayer loan of £1.7 billion to cover the normal running of the firm until a buyer could be found.
He has been criticised by MPs for continuing to receive a £250,000 salary to head up the supplier – effectively paid for by the taxpayer.
The announcement of his departure comes as the Government is considering offers for the firm, following a deadline of June 30 that was earmarked for closing bids.
It is understood the Government is hoping a deal can be agreed over the next month.
Advisory firm Teneo was hired as special administrators in order to oversee the firm’s insolvency.
It later hired experts from Lazards over the launch a sale process, which drew interest from a number of major suppliers.
It is understood that British Gas owner Centrica dropped out of the running in June.
Rival supplier Octopus is believed to be left in the running alongside Masdar – an energy company from Abu Dhabi.
When Bulb collapsed it had around 1.6 million customers on its books, meaning it was too big for the Government to allow it to go through the normal process that suppliers enter when they fail.
The taxpayer bailout was the biggest since Royal Bank of Scotland, Lloyds Banking Group and Halifax Bank of Scotland in the 2008 financial crisis.
Bulb went bust as it had not pre-bought enough energy in advance before prices shot up last autumn.
This left it unable to buy energy at a cheap enough price to cover the rates it must charge under the Government’s price cap.