The US forces had officially replaced the M3A1 Scout Car by the time of the Ardennes offensive. The only photo that I have ever seen of a US M3A1 Scout Car in the ETO was in the 3rd Armored Div. history "Spearhead in the West" where troops are seen removing waterproofing from one. In all my years of looking at photos of US military units in WW2 I have never seen a photo of a US-operated M3A1 in combat in Europe in WW2. One learns to not state catagorically that there weren't ANY, but they would be up there with hens' teeth in rarity, if any were used.
Yes, there wee quite a lot of Scout Cars in pre-war training, in North Africa and in Sicily. I'm not sure of when the last one's in Italy were replaced, but they don't show up in photos of US forces in Italy.
The Free French got lots of Lend-Lease and "hand me down" equipment and they seem to have had M3A1s longer than the US, plus some British armoured car regiments used them later than US units did.
In US Army service, by 1944 the M3A1 was replaced by the M8 armored car, the M20 armored utility vehicle or halftracks. US production capacity and transporation allowed units to replace obsolete equipment faster than any other army of WW2.
So, BBA16 can be many things, but should not be a US vehicle from the Battle of the Bulge.