In April 2008, Bu and Ni Hua became the second and third Chinese players to pass the 2700 Elo rating line, after Wang Yue.

At age six, Bu was first introduced to chess by an elder cousin (his grandfather was a strong xiangqi player), and his interest grew with his compatriot Xie Jun's women's world championship victory in 1991.

A sponsorship contract with a mineral water producer of his home city Qingdao enabled to him in 1999 with his coach Ji Yunqi to travel to Europe to take part there in several international chess tournaments.

Also in 2000, Bu defeated the Azerbaijani talent Teimour Radjabov 6+1⁄2-1½ in an eight-game Future World Champions Match competition in New York.

Radjabov had beaten Bu in the two game final of a Cadet's event held earlier in the year on the Kasparovchess.com site.

Although one of the favorites to win the tournament, he lost in the first round to American life master Shearwood McClelland III in an upset, before rallying to finish with 5+1⁄2/9.

[6] In 2006 Bu won the 9th World University Chess Championship in Lagos, Nigeria on tiebreak over Ni Hua, after they both scored 7+1⁄2 /9.

[8] In October 2007, he won the Blindfold Chess World Cup in Bilbao by a 1+1⁄2 point margin, defeating strong Grandmasters Veselin Topalov, Magnus Carlsen, Pentala Harikrishna, Judit Polgár and Sergey Karjakin in the process.

[9] In January 2008, at the 6th Gibtelecom Chess Festival in Gibraltar, Bu came joint first scoring 8/10 (+7−1=2; Elo performance 2834) but lost on the two game blitz play-off tie-break to Hikaru Nakamura.

In his super-tournament debut in Sofia, Bulgaria at the Grand Slam M-Tel Masters (category 20) tournament on May 7–18, 2008, he came fifth out of six players (Levon Aronian, Ivan Cheparinov, Vassily Ivanchuk, Teimour Radjabov, Veselin Topalov) having scored 3/10 (+1−5=4; Elo performance 2594).

A final round draw with Hou Yifan allowed Li Chao to catch him with 6/9, but Bu won the tournament on tiebreak with a performance rating of 2740.

[19] In June 2012, Bu won the 3rd Hainan Danzhou GM tournament on tiebreak over Ni Hua and this victory earned him the last spot in the Chinese team for the Istanbul Chess Olympiad.

In July 2014, he first tied for first with Ding Liren, placing second on tiebreak, in the 5th Hainan Danzhou tournament[21] and then won the Politiken Cup in Helsingør, Denmark with 9/10, a full point ahead of the field.

[25] In March 2024, he won the strong Shenzhen Masters event with 4.5/7, earning notable victories against Arjun Erigaisi and Anish Giri.