Ideally, carry a real basket, or a bucket, and set the berry basket into that, safely away from your heavier, bulkier purchases. Failing that, I’d put the basket in a paper bag, or leave the plastic bag open to the air. In hot weather, berries sweat if they are in a plastic bag. If, when you get home, you refrigerate them in that bag, or any other airtight container, before that moisture evaporates, you are setting them up to mold. Let the basket sit on the counter - better yet, with a fan blowing on it - for a while. Transfer the berries to a plastic container and lay a paper towel over them before applying the lid, which should be left open a crack. Refrigerate. After a few hours, remove the towel and dry off any condensation on the underside of the lid before sealing it completely.