I'd hoped for more responses here, but that's ok.
I'm no big band drummer, nor do I have more than a cursory knowledge of the tune in question.
I thought Mr A's answer was spot on however.
It's also occurred to me that my perceptions are skewed by the fact that I'm listening to the original as it was recorded with 1939 technology. A recording of that same performance with modern technology might sound very different.
Yes, I've had difficulty deciding what to play on 1960's pop style material.
They primarily miced the drums with a couple of overheads, or a single mic and the spill of the drums went into other mics for the orchestra or vocalist. Hence, the snare and cymbals are the most audible drum sounds on those old recordings.
If you play a similar part with a modern, focused bass drum, it can sound terrible wrong. The alternative is to play no bass drum at all, which also seems wrong.
In the end, I try to play a modern-ish part with a very light bass drum touch.
Sorry for the tangent.........