Edit to significantly revise earlier post:
Bader was an Acting Wing Commander when he was shot down, then made a Temporary Wing Commander in the Autumn of 1945. According to his obit in the Times, he was commanding the Central Fighter Establishment at Tangmere from June '45, and was a Group Captain. In January 1946, the Gazette notes his backdated promotion to substantive Wing Commander [from the end of the war]. He is recorded in the Gazette of 6 Aug 1946 as reverting to the retired list as a substantive Wing Commander, retaining the rank of Group Captain - he must, therefore, have been an Acting or Temporary Group Captain for his appointment at CFE and wasn't confirmed in substantive rank, but permitted to retain it.
It is also worth observing that he appears to have remained on the retired list throughout the war, as he references I can read in the Gazette suffix his decorations with (Ret.)
As a throwaway observation, 12 December 1947 he put the following in the Personal column of the Times:
Group Captain Douglas Bader DSO DFC will be broadcasting an appeal on Sunday next, Dec. 14 at 8.25pm for the Disabled Ex Servicemen of both wars now at St David's House, Ealing and the Queen Alexandra Hospital Home, Giffard House, Worthing. Please listen in.