Todd, here’s the link to King County Juror info. Parking info about half way down.
Basically, there are nearby public lots they say are expensive and fill up early. But I think they have earlybird all day specials.
http://www.kingcounty.gov/courts/superiorcourt/juror.aspx
They have a few parking spots right next to the courthouse that a bike could probably squeeze in easy enough, but I have a vague memory of them being reserved (?), or at least not all day.