I love the area, and get there about once a year or so (in fact, I'm going to be around Humboldt Redwoods State Park in a couple of weeks). I've been down Bald Hills Road several times, including a couple of months ago. It's a good-quality graded dirt road that should be fine in any passenger car (except maybe extremely low-clearance sports cars) so you should be fine. A little bit of pothole-slaloming, but relatively little. Mostly, it's pretty fast for a dirt road. I should add the caveat, though, that I've only taken it from 101 to the Tall Tress access road, not further to Weitchpec, so I don't know for sure that it's the same quality all the way along. If you're driving during the dark, though, I'd take it slowly and carefully to avoid the worst potholes, but I wouldn't call it crazy.
While you're in the area, though, don't forget the other redwood state parks in the area, which are every bit as good as the national park. One would normally think the national park would be the best bit, but in this case the state parks were there first, and the national park only took the best bit that was left over. Prairie Creek Redwoods State Park, Jedediah Smith Redwoods State Park, and Humboldt Redwoods State Park are all at least as good as the national park. I'd particularly recommend Fern Canyon (in Prairie Creek), Howland Hills Road to Stout Grove (in Jed Smith), and the Rockefeller Forest (in Humboldt).
Also, the town of Eureka on the coast has a handful of great overwrought Victorian houses that are very photogenic if you like that sort of thing. (And an excellent though pricey restaurant at the Hotel Carter.)