Yeah, you may want to check that plan with the rangers. Generally, if you leave the wilderness to catch a shuttle bus, you are required to get a second permit to re-enter again. That's what you are doing on day 4.

I like Bobito's suggestion of just spending the night at the backpacker's campground, then catching the bus to Tuolumne Meadows.

If you want to keep backpacking, you can also make this a loop by hiking up Lewis or Fletcher Creek over Vogelsang and Tuolumne Pass, then back to Tuolumne Meadows.

You are hiking some of the most popular trails in the park, so expect to see lots of people--and that also means that your permits are more likely to be checked by a ranger on the trail. But once you get on the trail, the actual route, including your campsites, are not in question. They just want to make sure that you are starting on the right trailhead (and that you have a permit to climb Half Dome).

You'll have a great time. Make sure you have bear canisters. They rent them very cheaply at the wilderness offices where you get your permits. Use them. Bear incidents in Yosemite have gone down like one of those big waterfalls since these kinds of preventive measures have been put in place.