Thanks for all the advice.

In the past I've just been using my garden hose to spray the underside as best as I can, for like 15 minutes. This is with the car sitting right on the driveway, and for sure there'll be spots that I can't reach.

So I was thinking, maybe the dealers have a standard job for this... putting the car on a hoist to get the underside really really clean? If they do, would they be charging the same hourly rate for this kind of 'detailing work'?

Their shop rate for repairs runs about $120/hour now, and from the advice above, it seems to be a foolish idea to take it to the dealers.