The 18-year-old midfielder collected the ball on the edge of the Arminia Bielefeld penalty area, dribbling past three defenders before chipping in.
Emre Can and Mats Hummelm also scored before Bellingham sealed it, the hosts scoring a consolation late on.
Bayern won 4-0 against Hoffenheim for a third thumping win of a superb week.
Poland striker Robert Lewandowski scored his 10th goal in nine Bundesliga games this season after Serge Gnabry gave the hosts a first-half lead.
Substitutes Eric Maxim Choupo-Moting and Kingsley Coman netted late goals to seal the victory.
After thrashing Bayer Leverkusen in a 5-1 win last weekend and beating Benfica 4-0 in the Champions League on Wednesday, the German champions again cruised to victory despite the absence of boss Julian Nagelsmann, who was quarantining at home after testing positive for Covid-19.
However, the 34-year-old still had an input after setting up what he called an ‘analysis centre’ in his home kitchen and passing on instructions to his assistants.