This may already be obvious, but how about a large sponge and a bucket?
It may take a weekend, but you will get rid of it without just
spreading it around or flooding your basement.

wrote:
My basement has flooded in the past and has a fair amount of
dust that is difficult to remove. Using a wet-dry vacuum doesn't get
all of the dust. Using a broom is only moderately helpful. I am
thinking of using a pressure washer, but I hate to introduce water to
the basement. Does anyone have any ideas as to the best way to clean
it?

Thanks,

JD