Ferrari got down to work at the outset, yet it was Bottas who laid down the first marker, his soft-shod W10 lapping in 1m31.169.
Though first practice at Sakhir offers unrepresentative conditions compared to qualifying and the race, which take part in the desert's cooler twilight, it was a hugely encouraging start to an all-important weekend for Ferrari. "I am really looking forward to what I'm sure will be a great experience".
Leclerc closed on Vettel in the closing stages of the season-opener in Melbourne but when he asked if he could attempt a pass for fourth place, his engineer told him to back off.
Mick Schumacher rose to fame in 2018 when he secured the F3 championship title while racing for the Mercedes-powered Prema Powerteam.
There is a feeling in the paddock that Bottas, winless last season, is boasting a meaner streak in 2019, but Hamilton said: "He is the same guy as he was a year ago, and I never thought he was a weak person". The last driver to run with Hamilton's "44" was also British, albeit a little-known one - a man named Tony Trimmer of Melchester Racing used it en-route to failing to qualify for the 1977 British GP.
There was an incident near the end of P1 when the nervous-looking Italian driver Giovinazzi tried to manoeuvr past Hulkenberg's Renault and bumped his front left wheel into the German's auto.
In a bid to change fortunes this year, the team replaced struggling team principal Maurizio Arrivabene with Mattia Binotto, formerly Ferrari chief technical officer. Michael Schumacher holds the record for race wins with 91 and is second for pole positions behind Lewis Hamilton.