The German, who is chasing his fifth victory in a row after winning Formula One's season-opener in Australia and the last three races of 2015, led both sessions with triple champion team mate Lewis Hamilton second.
Rosberg's best lap of one minute 31.001 seconds, in the floodlit evening session at the Sakhir circuit compared to Hamilton's 2015 pole of 1.32.671.
"I couldn't wait to get back in the car after a great weekend in Melbourne and I felt really good out there," said Rosberg.
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"It's been an encouraging first day for the team. We were very quick on one lap and also on the longer runs, so I'm really looking forward to qualifying and the race."
Hamilton, winner for the past two years in Bahrain, was the only other driver to lap below the 1:32 mark with a best effort of 1:31.242 and he agreed the Mercedes was performing impressively.
"There were no surprises or issues to report throughout both practice sessions, which is always a good sign," said the Briton. "There's some work to do tonight in terms of finding a few improvements from the car and also my driving style."
Jenson Button produced a third best time of 1:32.281 on the super-soft tyres, his lap just what McLaren wanted in the home of their major shareholders.
Button said the pace was genuine, for a team who battled with backmarkers for most of last season, with a real hope of a top 10 grid position.
"It was only practice but it was a lot more fun than normal," he said. "Reliability-wise everything was good and it was fun to have a car that was enjoyable to drive."
Ferrari's Kimi Raikkonen had been third fastest in the afternoon practice, a hefty 1.834 off Rosberg's pace on the same soft tyres as the Mercedes pair.
The Red Bulls of Australian Daniel Ricciardo and Russian Daniil Kvyat were fourth and fifth in that same session but Toro Rosso's Max Verstappen and Raikkonen filled those places in the evening.
Ferrari's Sebastian Vettel, third in Australia, was sixth but pulled off the track and stopped late in the second session with a loose rear-left wheel.
"The nut is not on, that was the problem," the four-times world champion said over the team radio.
Belgian Stoffel Vandoorne got to grips with the McLaren ahead of his Formula One race debut as stand-in for the injured Fernando Alonso and was 18th on the 22-driver timesheet in the first session.
The rookie moved up to 11th after another 30 laps in the second practice.
Vandoorne, who flew in from Japan where he is racing in the Super Formula series this season, had not previously driven the 2016 McLaren.
Spaniard Alonso was ruled out on Thursday, after failing to pass a medical following his big crash in Australia, and could also miss the following race in China on April 17.
(Editing by Ed Osmond and Pritha Sarkar)
