Norris lapped the Sakhir circuit in a time of one minute 34.669 seconds in the new MCL40, with four-times world champion Verstappen 0.129 slower, but quickest after the first half of the day's running.
Verstappen was in his RB22 all day and completed 136 laps, however, compared to McLaren's combined 112 laps with Oscar Piastri doing 54 in the morning.
"They (Red Bull) are able to deploy far more energy on the straights than everybody else,” Mercedes team boss Toto Wolff told reporters at the break. “I mean, I'm speaking a second per lap, over consecutive laps.
”I would say that as per today on the first official day of testing, which is always with the caveat of that, they've set the benchmark,” added the Austrian.
Red Bull are racing with their own engine this season after parting from Honda.
Mercedes-powered McLaren said they had focused on gathering aerodynamic data, rather than mileage or lap times, to provide a broader understanding of the car's operating window.
"Positive day, lots learned and looking forward to getting back in the car tomorrow," said Norris. Piastri said all had run smoothly and felt he had a better handle on the car.
Ferrari's Charles Leclerc was third on the timing screens, ahead of Ferrari-powered Haas's Esteban Ocon (115 laps) and Piastri. Pre-season favourite George Russell was sixth for Mercedes.
Mercedes had an issue in the afternoon when Kimi Antonelli was in the car while the Aston Martin AMR26 didn't appear at all for the later stint.
Lance Stroll completed 36 laps before a data anomaly emerged in the Honda power-unit and stopped further running.
Williams made up for lost time by getting in 145 laps with Carlos Sainz and Alex Albon after missing the pre-season shakedown in Barcelona last month.
"Our intent all the way through was just making sure we did the mileage required to learn and understand about the chassis, the power unit, and to start flushing gremlins out of the system," said team boss James Vowles.
"There will be a lot of them, and these next three days are all about getting a good foundation to work from, and we can then build performance."
Newcomers Cadillac managed 107 laps, with Sergio Perez 14th of 18 drivers who set a time. Audi, the former Sauber team, had Nico Hulkenberg ninth fastest with 73 laps.