Joe Biden turned a commercial flight into a full-on meet-and-greet ... bopping around the cabin, greeting passengers, and even penning a sweet note for a young girl.

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A TikTok making the rounds on social media shows a girl, Cailyn, stunned the former prez is sitting just three rows behind her ... where he's seen casually posted up reading the paper.

Looks like Joey B and Dr. Jill looked to be flying in biz class, and Cailyn couldn't believe she found herself chatting with 46.

They even snapped a selfie in which the former prez flashed a wide grin.

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At one point ... Biden writes Cailyn a note, telling her it was a pleasure meeting her. Politics aside, it's a pretty unique scenario to find yourself flying commercial with a former POTUS.

The wholesome interaction appears to have gone down Wednesday ... with Cailyn adding in another clip, "Can't believe this isn't an April Fools joke."

We haven’t seen a whole lot of Biden since he left the White House, but the ol' politician in him obviously still loves working a room.

We'd say he's free to move about the cabin, but dude IS 83. Please keep your seatbelt fastened, sir.