Kroger is building a new store at 86th & the Monon Trail. I hope they will build safe, secure bike parking there.
Conceivably, you could drive to Kroger in the morning before work. Get your bike off the car and ride the Monon to downtown Indy, or Carmel, for that matter. In the evening, you get off your bike, you pick up some fresh food at the grocery, and you drive the rest of the way home.
If they have safe, secure bike parking, you could just leave your bike there every night, instead of schlepping it home with your car. That would be sweet.