Media playback is not supported on this device
The 18-year-old from Essex broke the tibia and fibula in his left leg after landing on a concrete floor while vaulting in November.
Less than a month before his injury, Bevan was part of the first British team to claim a World Championships medal, when they won silver in Glasgow.
"It hurt my head and heart knowing what I had done," he told BBC Look East.
"My coach tried to jump in front of me to stop me from seeing what had happened - but I had already seen it."
Bevan won a series of junior titles before he claimed bronze in the pommel horse at the 2015 European Games in Baku.
He had hoped to continue that progress at the Olympics in Brazil but, with only 247 days until the Games, he knows it will be a challenge to be ready in time.
"The most important thing for me is getting back to full fitness so I can carry on my gymnastics career," he said.
"I don't think the Olympic Games is fully out of reach, it is going to be tough, but there is still a small chance I can push for a place in that team."

Ardit Ferizi from Kosovo pleaded guilty to charges of providing material support to America's enemies, at a court hearing in Virginia.
The computer hacker shared the personal data of more than 1,000 American military and government personnel.
The jail term imposed by the US court is the maximum sentence for his crime.
Ferizi, who was known online as Th3Dir3ctorY, was arrested in Malaysia in October 2015 and extradited to the US in January this year.
Speaking after the verdict, US Assistant Attorney General John Carlin described the attack as carrying a very real and dangerous threat to US national security.
In a statement in June, the US Department of Justice said the case was the first of its kind and represented "the nexus of the terror and cyber-threats".
It said Ferizi handed the list to IS knowing it could incite the group to attack the individuals named in it.
Information about the names, email addresses, passwords, locations and phone numbers for about 1,350 military personnel and federal staff came from several servers that Ferizi hacked into.
He targeted both machines in US government offices and corporate computers.
After he has served his sentence, he will be deported to Kosovo and barred from re-entering the US.
Gymnast Brinn Bevan believes he still has a "small chance" of competing in the Olympic Games in Rio next summer.
[NEXT_CONCEPT]
A 21-year-old has been sentenced to 20 years in prison in the US after passing details on American military personnel to so-called Islamic State (IS).