(Reuters) -- BATS Global Markets, the U.S. exchange operator that withdrew its public offering Friday after a computer glitch sent its newly issued stock into a tailspin, should develop a "credible IPO plan" and go through with it in the second quarter, its founder and current director said.

BATS' own stock was to be its first listing. But the initial public offering on Friday ended up a disaster after a software bug briefly sent the price of the shares down from $16 to less than a penny, before trading was halted. Later in the day, BATS took the extremely rare step of withdrawing the IPO altogether.

Founder Dave Cummings also advocated suspending all bonus plans at BATS, writing in an open letter emailed to industry insiders on Sunday: "In this business, mistakes cost money."

BATS is an electronic exchange owned by many of the world's largest banks and trading firms. In the last decade it has taken on the New York Stock Exchange and Nasdaq in the trading of stocks and, recently, also wanted to challenge them in listings.

"This was a freak one-time event," wrote Cummings, also the outspoken chairman of Tradebot Systems, an electronic trading firm that like BATS is based in Kansas City, Mo.

"BATS management should develop a plan to go public in the second quarter, if possible," he said. "This might seem tough, but I believe it is the only way to move past the issue."

Cummings, who remains a BATS investor after stepping down as its CEO in 2007, said the deal would need to be re-priced. But he defended BATS' technological record and argued that the "botched IPO" does not have much long-term impact on earnings because the exchange has "solid fundamentals."

Late on Friday, BATS outlined how the bug set off a series of fast-paced glitches through the trading day, including a halt in the trading of Apple Inc shares and the cancellation of erroneous trades in both Apple and BATS stock.

The software code used for the IPO was new and lab-tested, Cummings said, but "bugs do occur" in the real world. "BATS just happened to discover a bug at the most embarrassing time possible."

The letter was titled "What should BATS do now?" Cummings, a trailblazer and fierce defender of electronic trading, occasionally sends such emails to finance executives, traders, regulators and journalists.

He founded BATS, an acronym for "Better Alternative Trading System," in 2005 with 13 employees. It now handles about 11 percent of all U.S. stock trading, runs an options market, and recently completed the cross-Atlantic takeover of alternative trading venue Chi-X Europe.

IPO underwriters included Citigroup Inc, Morgan Stanley and Credit Suisse Group, which along with trading firm Getco LLC and others are major BATS shareholders.

(Reporting by Jonathan Spicer; editing by Sofina Mirza-Reid)