Doug, I'm not a mountain biker, but I'd say riding to Washington Lake is very doable, I've seen bikes on this trail before. The trail gains 800' of elevation in the first two miles, just like Hyndman. Although the fourth of July trail winds and twists around a bit more, and there will likely be a few more people to dodge. Of course if you plan to start really early, that won't be an issue.
Should be no problem getting a large van to the trailhead. The road is really bumpy with washboards, but you don't need high clearance. And there's a big parking lot at the trailhead.
Best of luck on the climb,
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