A pickup in offshore drilling is swelling the orderbooks of the handful of helicopter operators that shuttle oil workers to and from remote rigs. Their stock prices, depressed after Big Oil's recent spending cuts, could also be readying for take-off. Bristow Group Inc plans to invest $1 billion this year to procure just some of the 300 new helicopters that Barclays estimates will be needed by the oil and gas industry over the next five years. "We will invest more in this one year than in the last two-and-a-half years combined," said Jonathan Baliff, the chief financial officer of Bristow who will take over as CEO on July 31. With a market value of $2.7 billion…