"Meet Ted. #behindthescenes," the actor captioned the black and white photo which features Efron on set taking a mug shot while wearing a white T-shirt and high-waisted pants.
The film, from Oscar-nominated documentary filmmaker Joe Berlinger, will be told from the perspective of Bundy's longtime girlfriend Elizabeth Kloepfer who turned him in to police.
The screenplay by Michael Werwie won the Nicholl Fellowship first prize. Producers include Nicolas Chartier, Ara Keshishian and Michael Costigan. Efron's Ninjas Runnin' Wild banner will also produce alongside Michael Simkin and Jason Barrett.
Actress Lily Collin, who plays Kloepfer, also released on Instagram the first photo of herself in character.
"Meet Liz," she wrote alongside the photo that features herself sitting by a telephone.
Extremely Wicked, Shockingly Evil and Vile does not yet have a release date.
Bundy, who raped and murdered over 30 young girls and women, was executed in Florida in 1989.