Car will probably be fastest, even with traffic. Public transport will take forever. It depends a little on exactly when you're going (like if it's spring break or a holiday Monday it'll be different than just any old business day Monday) but in the fall I did just what you plan to (Disneyland to USH on a Monday morning) and we left Anaheim at 6am in order to get to USH with time to park, go through security and be there before early entry started. Got there with about 15 minutes to spare. If traffic is lighter than usual, the drive might only be an hour, if it's bad, could be up to 2 hours, so assume the worst is my advice. If you're early you can get coffee or something in CityWalk.