Bluman was born in Medellín, Colombia. His father, Samuel, is an entrepreneur, and his mother, Orly, is an Israeli psychologist and social worker. He has a brother, Steven. His Polish-born Jewish grandfather on his father's side, a Holocaust survivor whose entire family was murdered, was in the Auschwitz concentration camp for three years and later emigrated to Colombia. His father's family is from Poland and Holland. His grandfather on his mother's side is Israeli, and his mother's family is from Israel and Hungary. Bluman attended Hebrew schoolgrowing up. When he was ten years old, he moved with his family to South Florida in the United States. An alumnus of Cypress Bay High School in Weston, Florida, Bluman earned an associate degree in business from Florida Atlantic University, attending on a full scholarship. In 2016 Bluman married Ariel Epstein, an amateur rider who represents Israel in competition. The two have a son named Avi, who was born in 2018.
Riding career
Bluman started riding horses at age three. In 2004, he won the Gold Medal FEI Children World Championship at 16 years of age. In 2007 Bluman moved to Wellington, Florida, where he started his professional riding career. Bluman relocated to Belgium in 2013, where he trained with Nelson Pessoa for two years.
Bluman has been riding on behalf of Israel since late 2016. He said
"Through it all, the one thing that has always remained with me is my culture; what it means to be Jewish and to come from a family who has had to go through the Holocaust. Israel means a lot to me. Israel is a country that accepts every person — it doesn't matter your sexual orientation, your race, your religion, your ideas. It's a country that embraces you without prejudice … This is an amazing philosophy of life from an area of the world where living is not so easy. I'm very proud and emotional when I think about representing the Israeli flag."
He was named the 2018 Rider of the Year by L'Annee Hippique. In May 2019, Bluman won the Rolex Grand Prix at CSIO Rome di Siena. Bluman, along with Ashlee Bond, Danielle Goldstein Waldman, and Elad Yaniv became the first Israeli equestrian jumping team to qualify for the Olympics. The team qualified for the 2020 Olympic Games in Tokyo by winning a 2019 qualification tournament at Maxima Park in Moscow, Russia. The team's coach, Dutch-born Jeroen Dubbeldam, won a gold medal for the Netherlands in the 2000 Sydney Olympic Games.