I did a loop hike a year ago January with 3 friends. We descended the South Rim via the S. Kaibab and returned via the Bright Angel. Here's a public link to my FB pics - the captions have logistical info as well.
https://www.facebook.com/media/set/?set=...mp;l=477d716e80

Buses run very early (at least by 6) but that can be verified by their GCNP website, or by a call to them. We left our vehicle at the main VC about 6 (just missed the previous bus) but caught the next one. There appeared to be some limited parking at the S. Kaibab TH itself. On the return, we caught a bus not far from the Bright Angel TH over to the main VC and got our vehicle.

We took 2 liters down, but could have easily done with one. Before re-crossing the Colorado (near the kiosk in one of the pictures) was potable water. There was also potable water at Indian Springs. The Backcountry Visitor Center (it's a separate building) can give you exact status of the water sources.

In terms of the north rim - there was a highway failure in the north - near Paige - but I have no idea what - if any impact - the failure will have on rim-to-rim shuttles.

Hope this helps.