More than 20 energy suppliers have failed in the last two months.
If the application is successful, Bulb, which has around 1.7 million customers, will be run as normal by administrator Teneo, until a potential buyer can be found, or until its customers leave.
In what has been dubbed by some as a too-big-to-fail alternative to Ofgem’s usual process, Bulb will keep serving customers.
The company is three times larger than any other energy supplier that has failed in recent years. Normally Ofgem simply lets a firm fail and moves its customers to a new supplier.
The regulator said: “Ofgem has applied to the court to appoint a special administrator to run Bulb Energy Limited.
“Customers of Bulb do not need to worry. If a special administrator is appointed, they will see no disruption to their supply, their price plan will remain the same, and any outstanding credit balances, including money owed to customers who have recently switched, will be honoured.”
The Department for Business, Energy & Industrial Strategy said: “Energy regulator Ofgem, with the Government’s consent, has made an application to the court. We do not comment on ongoing court proceedings.
“The Special Administration Regime is long-standing, well-established mechanism to protect energy consumers and ensure continued energy supply when a supplier fails.
“Bulb customers do not need to do anything, there will be no disruption to supply or current energy prices, and credit balances are protected.”
Business Secretary Kwasi Kwarteng said a special administration regime was a temporary arrangement “which provides an ultimate safety net to protect consumers and ensure continued supply”.
He told the Commons: “We do not want this company to be in this temporary state longer than is absolutely necessary.”
For Labour, shadow business secretary Ed Miliband said: “With so many companies going bust in just two months, something not happening anywhere else in the world, it points to a systemic failure of regulation. Firms took risky bets and were allowed to do so and the Government and Ofgem significantly deregulated the conditions of operation in 2016.
“Will the Business Secretary now take responsibility for the clear failure of regulation there has been and doesn’t it suggest there needs to be a proper external review of the regulation of the market.”
Since the beginning of September, 22 energy suppliers have failed. They were pushed out of the market by a spike in gas prices.
As a result of these prices, and a cap on what companies can charge their customers, businesses have been forced to sell energy for less than they bought it for.
Some of the biggest companies buy their gas far enough in advance that they have avoided the worst impacts of the price spike.
However those who have not have been placed under unprecedented pressure.
Labour MP Alex Sobel (Leeds North West) warned in the Commons: “We’re moving back to an oligopoly of energy companies who are increasing their profits whilst the supplier of last resort is socialising losses.
“What’s he going to do to fix the broken energy market?”
Mr Kwarteng replied: “I don’t agree with his characterisation. I don’t think we’re going back to an oligopoly, as he said. I’ve always maintained that competition is absolutely essential in this market.
“What’s happened is there’s been a huge mismatch between the wholesale price and the retail price cap, and the retail price cap is there to protect consumers.”
Liberal Democrat MP Layla Moran (Oxford West and Abingdon) suggested a “Northern Rock-style energy company to take on customers of companies that have gone under” if the current process is not working.