The plot in Budtameez is very loosely based on The Taming of the Shrew in which an impetuous and obstinate shrew is "tamed" into getting into a relationship by a suitor using various psychological torments to change her into a submissive and docile partner.

In Budtameez's retelling of this tale, the plot begins with Shyam Kumar, who plays the suitor in this film. Shyam lives in Allahabad with his stepmother and step-sister Beena. Apparently, Beena had met with an accident because of Shyam and requires the use of a wheelchair. As Shyam's stepmother keeps on niggling him to get a job, Shyam goes to Bombay in search of one and gets a job running the household of the wealthy Raja Bahadur Murti Sagar.

The story picks up with the introduction of Shanta, the "shrew" of the movie, who is Rajabahadur's orphaned granddaughter. Shanta has grown up hating men because her father was an alcoholic who abused her mother until she committed suicide. Understandably, Shanta has turned into an impetuous and ill-mannered person, particularly so to servants like Gopal, who works for the household.

Earlier Rajabahadur had bought in Rita into the household to get Shanta to mend her ways, but Rita's efforts have been unsuccessful. To make matters worse, Shanta's ego is relentlessly fueled by Devdas, who clearly wants to marry her. As part of his efforts to draw Shanta's attention, he persistently engages in weird behaviors, such as dressing up as characters like Robin Hood, and even a donkey. Fed up with his lack of success, Rajabahadur entrusts the task of reforming Shanta to Shyam.

Much of the remaining movie deals with Shyam's repeated attempts to tame Shanta. Things begin to change when Shyam and Shanta take a road trip. The introduction of retired Col. Jung Bahadur during the trip provides a defining moment that helps change Shanta's behavior. Slowly, but surely, Shanta and Shyam fall in love, much to the delight of Rajabahadur, who starts making arrangements for their marriage. Shyam returns to Allahabad to inform his stepmother and stepsister about the upcoming marriage.

The plot subsequently takes an unexpected twist. Rajabahadur receives an invitation for Shyam and Kamla's wedding. The question remains who is Kamla and why is Shyam rejecting Shanta and marrying her? What will happen to Shanta? The plot unfolds with the resolution of the complications that have developed because of this watershed event in the story.