Bizzarrini received an engineering degree from the University of Pisa in 1953. His thesis was the redesign of a Fiat Topolino, where he modified the engine for increased power and relocated it in the chassis for improved handling.

After graduating, Bizzarrini joined Alfa Romeo, assigned to the development of the Giulietta chassis. He was later able to move to the Experimental Department, receiving on-the-job training and becoming a test driver. In his words: "I became a test driver who coincidentally was also an engineer, with mathematical principles. I always needed to know why something fails, so I can invent a solution."

Giotto gained a reputation for identifying and solving problems and in 1957 left Alfa Romeo when he was head hunted by Ferrari, who were searching for a test driver.

Bizzarrini worked for five years at Ferrari in roles including Chief Engineer, having been promoted through the ranks Giotto’s responsibility increased, eventually becoming controller of experimental, Sports and GT car development. 

Bizzarrini developed chassis, engines, and aerodynamic dynamic solutions at Ferrari, working on notable projects including the 250 series. His masterpiece at Ferrari was the 1962 250 GTO. 

Ferrari needed a GT racer with improved aerodynamics over the 250 GT SWB. Tests started secretly on a 250 GT, chassis number #2643GT, Bizzarrini's personal car. This vehicle became a mule for the technical solutions later seen in the GTO. "We dubbed the car Il Mostro." ('The Monster').

Experiments with the SWB chassis had indicated considerable speed loss attributed to aerodynamic drag, so for the GTO Bizzarrini reduced the frontal area and increased the bonnet length, reducing both drag and the tendency to front lift at high speeds. 

Bizzarrini moved the engine well back and lowered it into the chassis (by using a dry sump lubrication system) improving weight distribution and handling. The result was racing success for the legendary Ferrari 250 GTO.

In November 1961, Bizzarrini was one of the "famous five" engineers who left Ferrari in the so-called "Palace Revolt", provoked by a disagreement with Enzo Ferrari himself.

In 1962 Bizzarrini founded Società Autostar, his own engineering firm through which he could bid for freelance engineering projects.

Bizzarrini was hired by Count Giovanni Volpi, owner of the Scuderia Serenissima, to upgrade a Ferrari 250 GT SWB (chassis number 2819GT) to GTO specification. Ferrari was upset with Volpi and do refused to sell him a GTO, so Bizzarrini had to acquire and modify a used vehicle to race.

Giotto further advanced his ideas from the GTO and with Piero Drogo of Carrozzeria Sports Cars in Modena developed an aerodynamically advanced body, even lower than the GTO with the roof line dramatically extended to the rear end, abruptly truncated to follow the Kamm aerodynamic theory. 

This car was reportedly completed in just 14 days and chassis number #2819GT was became famously known as the Ferrari Breadvan.

A year later Ferruccio Lamborghini commissioned Bizzarrini to design an engine for his new GT cars. After a dispute between Ferrari and Lamborghini Giotto was to receive a bonus payment for every 1hp more his engine could produce over the Ferrari V12 of the day. This Lamborghini V12 was first manufactured for use in the 350GT in 1964 and variations of the basic design were used in every V-12 Lamborghini until 2010 in the Murciélago SV.

Through Società Autostar Bizzarrini developed cars for Renzo Rivolta of Iso Autoveicoli S.p.A. including the Iso Rivolta IR 300 and the Iso Grifo. Through his work with Iso Giotto became friends with a young Giorgetto Giugiaro, this partnership has endured more than 60 years.

A dispute between Bizzarrini and Rivolta ended their collaboration, and led to Società Autostar building variants of the Iso Grifo under the Bizzarrini marque. This led Bizzarrini to change the name of Società Autostar first, in 1964, to Società Prototipi Bizzarrini and then in 1966 to Bizzarrini SpA.