It’s a Hollywood legend that Walt Disney felt some sort of malevolent glee in killing Bambi’s mom, and what that animated death would do to the children who saw it. But that’s only a legend.

P.L. Travers, the woman who wrote “Mary Poppins,” was a brittle, snobbish martinet and a humorless control freak. And that’s a fact. Stay through the credits of “Saving Mr. Banks” and hear for yourself.

Emma Thompson brings Travers to prickly life in “Saving Mr. Banks,” Disney’s amusingly testy and emotionally rich telling of Walt Disney’s courtly struggles with the dismissive writer as he and his dream factory turned her “Mary Poppins” into one of the most beloved children’s musicals ever.

The courtship — Tom Hanks plays patient, long-suffering Disney — is not an easy one. She is in the habit of barging into the movie/TV/ theme park mogul’s office. He is all charm and informality. He calls her “Pam.”

We meet Travers in London, her agent telling her she needs the money and must finally sell the screen rights to her most famous book.

Travers flies to Los Angeles and disapproves — of everything. The flight, the scent in the air, the hotel.

“Let’s make something wonderful,” Walt purrs.

“I won’t have her turned into one of your silly cartoons!”

Director John Lee Hancock (“The Blind Side”) keeps this courtship center stage, and tells the story of Walt figuring out why Travers (real name, Helen Lyndon Goff) is the way she is and what he can do to make this unpleasant and miserable woman happy.

The battles in the early ’60s in Burbank, Calif., deliver the laughs, and lots of them. Travers came to “supervise” the planned film, basically threatening to back out of the deal over the casting of Dick Van Dyke, over the inclusion of an animated sequence, over the silly, made-up-word songs of the beloved Disney house composers, the Sherman Brothers (Jason Schwartzman and B.J. Novack, a hoot), and other irritants.

It was never going to be “Supercalifragilisticexpialidocious.” Reserve that honor for the film that inspired it. But “Saving Mr. Banks” is still one of the best pictures of the year.