The Dutch 25-year-old was top of the timesheets before and after lunch at Sakhir as teams mainly focused on aerodynamics with prominent rakes attached to the cars in their first proper running.
Verstappen won 15 of 22 grand prix last year and will be chasing his third straight title when the 23-race season starts on March 5.
“We had a good day today, we completed a lot of laps which is what we wanted – almost three grand prix’s worth,” he said. “It was also a smooth day; we barely had any issues, and we could really focus on the car and try a few things.
“It’s nice to see how the car has evolved from last year.”
Ferrari’s Carlos Sainz was second in the morning, 0.294 slower but on top for a majority of the session, with Williams Alexander Albon third and doing the most laps (74).
Double world champion Alonso was soon up to speed at his new team in the later session, 0.029 slower than Verstappen who clocked a best of one minute 32.837 seconds and did 157 laps as the only driver to be testing all day.
Mercedes and Ferrari also sounded positive, with Mercedes boss Toto Wolff noting a buzz of excitement in the garages.
The Austrian said it had been a productive day and very different from 2022 when the team were wrestling with a bouncing, “porpoising” car.
The former champions had George Russell in action for the opening stint, with the Briton queuing up in the pitlane to be first out, before seven-times world champion Lewis Hamilton hit the track later on.
“He was generally happy with the car. It seems to be balanced in the right way. There’s no bouncing, which is good news,” said Wolff of Russell’s reaction.
“I think we have a solid base now to work from and try to optimize the car.”
Hamilton was sixth fastest and put in a hefty 83 laps.
New Ferrari team boss Fred Vasseur said his drivers were also happy.
“The first feeling was good. The most important was to do mileage and we had no issue. We were able to do the run plan and everything is going well so far.”
Sainz was third fastest overall, with team mate Charles Leclerc fourth and McLaren’s Lando Norris fifth despite losing track time for repairs to his car.
The red flags were waved after nine minutes when Brazilian Felipe Drugovich, standing in for injured Canadian Lance Stroll, stopped his Aston Martin on track with an electrical problem.
Aston Martin said Alonso would be in the car all day on Friday.
German driver Nico Hulkenberg started his comeback at Haas while Australian rookie Oscar Piastri did 52 laps for McLaren but propped up the timesheets.
“There is still a lot to learn and improvements to make but I think I’m getting there. It was good to get some laps on the board and everything felt pretty comfy,” said Piastri.