Probably hitching should be quite do-able, (and a lot cheaper), especially with a sign reading ' Horseshoe Meadows. Leaving the car at the Portal (good idea for when you return) and getting down to the HM junction should be easy - I would do it in a second.
The rest of the way though might take you a while, but as there is only one road destination - up to HM, and you are alone...With an obvious backpack...
Figure one full day for this, but not surprised if probably shorter, especially if done on a weekend.
FYI, the time we did this, (5 years ago) it was only $160 - inflation.
Mountainman who swims with trout