MODS, suggest that you transfer this query to Non-airfield sites.
My notes indicate that Bures was a Forward depot (as opposed to a Main Depot) and that it was manned by 2108 Ordnance Battalion (Aviation) Sp(?).
So, it would have been supplying to USAAF airfields in the region. You say that logistically, you would havethought 8AF and 9AF supply systems would have been separate. To me it would have made sense to have one supply system for both to avoid duplication of effort but, I accept that 60 odd years ago the inefficient 'them and us' system prevailed.
So, looking at how the 8th AF was supplied (from my notes). The US Army Services of Supply arranged with the British Government to establish muntions storage sites in 1942. The first site was at Barnham in June 1942 and in July 1942 Sharnbrook. These sites supplied the 8th's initial operations. Next came Braybrooke, Melton Mowbray(?) and Wortley (aka Scouts Dyke) in July 1943 but the the last two became truck depots. Earsham was next in Aug/Sep 1943.
Records indicate that generally 1AD was supplied by Sharnbrook, 2AD by Earsham and 3AD by Warren Wood (at Barnham) as you thought.
Bures was setup sometime in 1943 and supplied 9th AF Bomb Groups. After the departure to France of B26 and A20 bomber units this site then supplied local B17 units with 'remaining munitions' (implies Bures was not restocked). Presumably 8AF bases were also supplied.
The next note that I have I don't fully understand, it was written a long time ago and the cross reference (sources) is not to hand. But, it indicates that the USSTAF (United States Tactical Air Force), early in 1944, took over the 8th AF Service Command HQ and BADAs and assumed control of all munition stores. The 8th AF still got their ordnance from these stores but no longer controlled the manpower.
Hope this helps.