great dayhike, took us 14 hrs at comfortable 2.1 mph incl rests.
you can park for free overnight(s) downhill from MMI and ski area on the very wide shoulder on either side of the main road for several 100s of yards. Done it plenty of times in summer.
The pay area is marked with logs and signs and easy to avoid.
If you are leaving Mammoth at say 5 am for your early start, there will be no shuttle that early to AM. Before 7am you can drive your car to AM. I have left cars there before while hiking or backpacking but don't know what 2009 rules are. If you are wondering how to retrieve your car after returning from TM to MMI the next day, you can take the shuttle from MMI to AM as long as it is between 7 am and 7pm.
Reds Shuttle goes by every half hour I think in summer - have used it plenty of times, Agnew is stop 1 from the top. Buy a day pass(you only would use half of it) at the building near the Mammoth statue.
Although I have done AM to TM via JMT, via River Trail, and via PCT/High Trail, I prefer via High Trail with more expansive views and (I think) less up and down on an otherwise long day. The least desireable option is the entirely forested River Trail, but it depends on what you like of course. Have fun. Harvey