At the 1996 Atlanta Games, Bloom placed 31st in individual epee. He was a member of the U.S. épée team that finished 8th. They were eliminated in the quarterfinals by Italy, 45-44.
He tore the anterior cruciate ligament in his right knee while playing basketball in 1999, and was unable to participate in the World Championships in Seoul. He told no one that he was injured, and flew to Seoul with the intention of competing, but changed his mind. As it was too late to arrange for an alternate, team coach Michael Marx took his spot. The team finished 15th, which was not good enough to qualify for the team épée event at the 2000 Summer Olympics. Bloom went on to earn enough World Cup points to enter and win the Olympic Zonal Qualifier in Buenos Aires on an individual basis, and thus was the only American entered in the men's épée at the Sydney Olympics.
At the 2000 Sydney Games, Bloom lost in the 2nd round of individual épée to Arnd Schmitt, the top-ranked épée fencer in the world. Bloom finished 29th.