Once you've set a Due Date for a Card, you can also choose when to receive your Reminder Notification in Buckets. The Reminder will automatically assign itself to your Card.
You can also add a Reminder to a Checklist or an individual Checklist item in a Buckets Card.
To add a Reminder to a specific Checklist item, use the drag-drop feature to move it down to that item. You can also add a Reminder to a Checklist item by clicking on the clock icon that appears when you hover over that item.