I'd rule out staying at Sonora Bridge. Its a nice campground, but unless the ground water has improved you need to treat it as a dry camping site. About ten years ago the water table shifted and whatever feeds the local hot springs got into the Sonora Bridge wells and the water is sulfurous. Bootleg is a noce spot along the river, but you need to put up with the noise of 24x7 traffic along 395. My own personal recommendation is to stay at Honeymoon Flat Campground. Its on the road from Bridgeport to Twin Lakes, or go camp up along Desert Creek on Risue Pass Road - I drink from the creek all the time being it's source is snow melt. Leavitt Meadows Campground is another good one.
I'm up for doing a ride one of those days. Either Mt. Patterson, or showing whats out around Bodie/Aurora/Pine Grove. Is your 450 plated? What type of range do you get from a tank of gas?
When the going gets weird, the weird turn pro