After years of relative equilibrium, the job market for nurses is heating up in many markets, driving up wages and sign-on bonuses for the nation’s fifth-largest occupation.

The last nursing shortage more than a decade ago ended when a surge of nursing graduates filled many positions, and the financial crisis of 2008 led older nurses to delay retirement. But as the economy improves, nurses who held on to jobs through the uneven recovery are now retiring or cutting back hours, say recruiters. The departures come as demand for nurses has increased, thanks to expanded insurance coverage from job growth and the Affordable Care Act.

“We’re having a retirement wave,” said Jane Englebright, senior vice president and chief nursing officer for HCA Holdings Inc., HCA -2.17% the largest U.S. hospital company, with hospitals largely scattered across the South. HCA has reported wage increases for nurses in some markets, but she declined to say where.

National numbers show a stable nurse workforce in recent years, with the average U.S. nurse’s wage flat and enough new graduates to offset retirees. Yet national numbers lag the emerging regional pockets of shortages, say employers and workforce analysts. Peter Buerhaus, a health-care economist and nursing professor at Montana State University, said he is hearing of strains in areas, and he and colleagues forecast greater shortages in New England and along the West Coast in coming years. In Pennsylvania, Florida and Nebraska, the proliferation of new nursing jobs outside of hospitals has helped strain supply, say several hospital operators. In Iowa, surging demand for hospital care has outstripped the labor market. In Texas, hospitals cannot hire fast enough to match population growth.

For hospitals, which employ more than half of the nation’s 2.8 million nurses, too few nurses means a scramble for essential staff and higher labor costs that can squeeze bottom lines. Costly temporary nurses and overtime pay are driving up expenses, say hospital employers. Signing bonuses—some $10,000 or more—are increasingly common in states like Texas, California and Florida, recruiters and labor experts say.

Nurses are “very confident,” said Brian Scott, chief financial officer for temporary staffing giant AMN Healthcare Services Inc., in September at an investor conference. Nurses push for the “best wages and benefits,” he said. Nurse recruiters on the company’s payroll have increased 79% since the end of 2013, to keep up with growing demand.

Sandra Brown, 49 years old, graduated from the Chamberlain College of Nursing in Atlanta in April. As she prepared to leave school “interest was phenomenal,” she said. Ms. Brown chose WellStar Health System, though another employer paid more. The 11-hospital system, based in Atlanta, let her pick among several openings, with additional on-the-job training. She received a pension, a $10,000 sign-on bonus and concierge services to help with grocery shopping and other errands.

“There is so much out there,” said Ms. Brown, who continues to hear from recruiters.

Community Health Systems Inc., the nation’s second-largest hospital company by hospitals, recently raised nurses’ wages in some markets, said Larry Cash, chief financial officer, at the same investor conference. Wage growth edged upward to between 2.5% and 3% this year from 1.5% to 2% two years ago, Mr. Cash said. The Franklin, Tenn.-based company, which mostly operates across the South and mid-Atlantic, declined to specify where demand is tightest.

Geisinger Health System, which operates a dozen hospitals in Pennsylvania and New Jersey, began offering nurses with as little as one year of experience sign-on bonuses up to $15,000 in September, said officials there. Geisinger also urged its nurses to reach out on social media to prospective candidates to promote the offer, said Julene Campion, Geisinger’s vice president of talent management. “We think we’ve piqued some interest,” she said.

Sign-on bonuses are “back with a vengeance,” said economist and University of California San Francisco nursing professor Joanne Spetz, who studies the California nurse labor market. Nursing vacancies at California hospitals increased 40% last year as nurses retired and newly insured patients sought care, a Hospital Association of Southern California survey shows. Nationally about 2.5% of nursing positions listed in September at career website Indeed.com offered job seekers a signing bonus, up from 0.5% in 2013.

The prospect of nursing shortages isn’t as dire as the last shortfall more than a decade ago, when the U.S. Department of Health and Human Services said the nation lacked 110,000 nurses. Labor experts say the influx of new graduates is expected to offset the wave of retiring nurses in the coming decade. But projections by Mr. Buerhaus and other researchers, based on analysis of demographic trends and nursing graduation rates, show that won’t be enough to meet growing demand in the coming decade.

Write to Melanie Evans at Melanie.Evans@wsj.com