From January to March, Apple’s CEO racked up $127,000 in expenses on his private Gulfstream V jet, according to the Form 10-Q Apple (AAPL) filed with the SEC on Wednesday.

That’s not much compared with the record $550,000 Steve Jobs burned in the fall of 2007, when Apple was busy negotiating with overseas cell phone operators to carry the iPhone.

But it’s a lot more than the $4,000 reimbursement he put in for all of fiscal year 2009, much of which he spent recovering from a liver transplant.

Back in February 2008, Morgan Stanley’s Katy Huberty cited Jobs’ frequent flier miles as a reason to be bullish about the company’s stock. Jobs, she wrote, is “integral to negotiations with international carriers and supply chain partners.”

Apple managed just fine while Jobs’ jet was grounded, although investors will probably be happy to learn that it’s flying again. We know Jobs made trips to the East Coast to demonstrate the iPad to New York-based publishers. Whatever else he might be up to is not revealed in Apple’s Form 10-Q.

[Follow Philip Elmer-DeWitt on Twitter @philiped]