Bearman got the call up on Friday morning after Carlos Sainz was diagnosed with appendicitis.
The Spaniard underwent surgery on Friday in Saudi Arabia and is recovering in hospital.
At the track, Bearman took part in an abridged opening practice session interrupted by a late red flag ahead of a maiden qualifying session for the Scuderia.
The 18-year-old is the first rookie to debut for Ferrari in over 50 years and the youngest driver to have ever started a race for the famous marque.
“I was thinking this morning when I heard the noise, what causes appendicitis,” Doohan joked when asked about Bearman’s promotion on Sky Sports.
“Not really. I don’t wish that on anyone!
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“I was very happy for him [Bearman]. It was a big task, but to be honest, seeing and watching, he handled it very, very well.”
Bearman ended the opening practice session 10th fastest, though his qualifying simulation lap included cutting Turn 22.
It was the only blemish of the session and his only soft tyre run in an hour in which he stole the spotlight.
Bearman is Ferrari’s nominated reserve driver.
The Englishman competes in Formula 2, where he raced against Doohan last year.
Doohan is not competing this season as he focuses his efforts on supporting Alpine as its reserve driver.
He could, therefore, only look on in envy as Bearman, who’d been fastest in F2 qualifying on Thursday, received the call-up to make his F1 debut.
“Straightaway, he was on the pace very well,” Doohan noted.
“He actually finished six or seven-tenths away from Charles [Leclerc], which in the big picture could seem like a lot, but that was his first time and his only lap on that soft set of tyres.
“To go out there and I think do that is no small task.”
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