Bob's already given you lots of good information. He made it clear, but I'll reiterate that the road to Mineral King is not Sunday morning drive. I drive A LOT. I LOVE road trips. I didn't like driving that road. it was about only 1.5 lanes wide and curvy enough that I spent the whole drive tensed up for those (rare) times when I had to hug my side of the road when opposing traffic came around the corner.
Also, when I did a week-long loop out of Mineral King, we got hit by a black bear one night. I was 19 and stupid and scared. Now, I know how to greatly minimize bear interactions and later learned that a little attitude goes a long way with black bears in California. That bear would now be more traumatized by any interaction than I was, but that seems to be an acquired skill.
I wouldn't expect any problem with dried, packaged foods. Declare them on the forms they give you, but if you want specialized stuff, I'd bring it. But US food prices are lower and California produce fresher than anywhere else. I'd suggest you stop at a Trader Joe's (yuppie food, grab some sushi for the drive and some wraps for your first day) in LA or Fresno and then a Safeway (standard supermarket) in Fresno.
Your rental car should have plenty of range so you only have to top off in Fresno – the price of gas increase with elevation and distance form the Interstate.
Long ago, I saw a figure that SEKI had $60,000/year of auto damage by bears. The biggest avoidable issue was an ice chest visible through the windows. A black bear can peel off a car door. The trunk is much safer. I've never had a problem with food in the trunk, I haven't heard of any such problems, but if I had smoked fish or salami, I'd keep it with me or get it in a metal storage locker or simply not bring it. When I've seen a black bear go for one pack out of 10, it was always the one with the salami in it.

