In 2003, he tied for first with Vladimir Burmakin, Eduardas Rozentalis, Philipp Schlosser, Alexander Areshchenko, Jakov Geller and Evgeny Miroshnichenko in the Cappelle-la-Grande Open, finishing sixth on tiebreak.
[2] In 2004, Bocharov took clear first place at the Masters tournament of the 14th Abu Dhabi Chess Festival.
[6] At the 2009 Voronezh Open he tied for first with Sergey Volkov, Igor Lysyj, Aleksandr Rakhmanov, Valerij Popov, Denis Khismatullin, Dmitry Andreikin and Dmitry Kokarev, placing eighth on countback.
[9] He played for Novosibirsk's team "Siberia" (alongside Vladimir Kramnik and Levon Aronian among others) that won both the Russian Team Chess Championship Premiere League[10][11] and the European Chess Club Cup in 2015.
[13] In 2020, Bocharov placed 2nd-6th in the 1st Mukhtar Ismagambetov Memorial along with Shakhriyar Mamedyarov, Nodirbek Abdusattorov, Kazybek Nogerbek, and Davit Maghalashvili, with a score of 8.5/11.