Bischoff learned chess as a 11- year-old. In 1975, he was the unofficial champion and German pupils made rapid progress. In the World Youth Championship 1980 in Dortmund, who won Garry Kasparov, Nigel Short Bischoff won after the split third place. 1982 Bischoff became International Champion.
According to standards in Lugano, Kecskemet and Bad Wörishofen him the FIDE awarded the title of Grandmaster in 1990. In 1997, he won the tournament in Recklinghausen before Jens -Uwe Maiwald and Ludger Keitlinghaus.
Klaus Bischoff is German record winner at the national championships flash and is regarded as a solid team player. In 2000 he won in Essen together with Vadim Zvyagintsev and Alexei Drejew, also in the same year in St. Ingbert, 2002 Baunatal, 2003 in Bad Arolsen. 2003 Bischoff won for the first time discharged German Internet blitz chess championship, inter alia January Gustafsson and Robert Hübner. 2003, 2004 and 2005, he won the German championship in rapid chess. 2013 in Saarbrücken, he won the German Individual Championship.
Bischoff took part in six Chess Olympiads, and was founded in 2000 with the German national team silver medalist in Istanbul 2000. With the national team he participated in three European Team Championships and won bronze at the European Championships in 1989 and 2001. In the 2001 tournament in Leon received Bischoff the gold medal for the best individual result on 4 board.
Klaus Bischoff played in the German Chess League 1981-1995 FC Bayern Munich and was with this in 1983, 1985, 1986, 1989, 1990, 1991, 1992, 1993 and 1995 German team champion. From 1995 to 1999 Bischoff played at SG 1868 Alekhine Solingen and was with this 1997 German team champion. Then he played from 1999 to 2003 at King Plauen, from 2003 to 2006 and again in the 2008 /09 season at the TV Tegernsee, in the 2006/07 season at TSV Bindlach Shareholder and 2009-2013 in the sports friends Katernberg.
In the Austrian State League A ( to 2003 ) and 1st League ( since 2003) played Bischoff 1993-1997 at SC Inter Salzburg, 2001-2008 at SC The Klagenfurt, 2008-2010 in wood Dohr Semriach. Since 2011 he plays for SK Sparkasse Jenbach, with whom he became in 2013 an Austrian team champion. In the French Top 16 ( up to 2002 National I) Bischoff played until 2006 Echiquier's Nanceien, in the British Four Nations Chess League in the 1995/96 season at the British Chess Magazine and in the 1998/99 season at Home House.