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Rosberg, 24, who is 17 years younger than the former Ferrari hero, clocked a best time of 1min 55.409sec to outpace his nearest rival Lewis Hamilton in a McLaren, by four-tenths of a second.
Schumacher, back after three years in retirement, was third fastest ahead of Hamilton's new McLaren team-mate defending world champion Jenson Button.
All of the four leading cars were powered by Mercedes engines.
Sebastian Vettel, who finished runner-up last season in the drivers' championship, was fifth for the Red Bull team with young compatriot and Formula One debutant Nico Hulkenburg, 22, who succeeded Rosberg at Williams, clocking the sixth best time.
With Rosberg, Schumacher, Vettel and Hulkenberg Germany had four drivers in the top six.
On a very warm day at the Sakhir circuit, with air temperatures rising beyond 30 degrees Celsius, the times were unpredictable and unreliable as signals of likely performance in qualifying on Saturday.
This is due to the new rules this season which have removed tactical refuelling and put the onus back on tyre performance.
It is very difficult to know what fuel loads the cars were carrying on Friday - and therefore what their real relative performances were like.
This may help explain why the Ferraris of Brazilian Felipe Massa, back in action for the first time since his horror accident at last year's Hungarian Grand Prix, and two-times champion Fernando Alonso, making his debut for the Italian team, appeared to struggle before clocking the seventh and ninth fastest times.
Like many other teams, Ferrari were concentrating on long distance runs with heavy fuel loads.
They sandwiched the Russian new boy Vitaly Petrov in the leading Renault while his team-mate Pole Robert Kubica was down in 15th place.
Australian Mark Webber in the second Red Bull was 17th fastest after being stopped early in the session with driveshaft problems.
This at least left him ahead of the cars from the three new teams as the Lotus, Virgin and Hispania outfits worked on reliability, the latter managing only to give Bruno Senna, nephew of the three-times champion Ayrton Senna, 17 laps while his team-mate Indian Karun Chandkok did not run because his car is not yet ready.
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