I've tried this twice before ...
Reading Orange's book 'Dowding' there are two unsettling pieces of information.
The first (p200) is double-barrelled ... on 30 August 10 Hurricanes led by Bader attacked a force of 100 Luftwaffe aircraft, shooting down 12 and damaging others and without suffering a single bullet hole in return. Allegedly there is no other evidence of this air battle. Further down the page is an observation that squadrons in Bader's wing claimed twice as many victories as other squadrons, and that these later results are known to be inflated. The citation is to Orange's book 'Park', which I don't possess.
The second (p226) is to fighter sweeps over France where in 1941 the RAF claim June-December was 731 fighters destroyed, whereas German losses for all of 1941 came to 103 in combat + 50 odd to accidents and c.
So the question is 'how many German aircaft did Bader likely shoot down?' His claim was 22