That initial drying needs about 2-3 weeks in a dark, dry spot like a closet. It doesn't really save the scent forever though... the oils that make the smell just fade slower without sunlight and heat beating on them. My grandma's lavender from last year is mostly just pretty dried flowers now. The dark closet just helps it keep some smell for a good while longer.
Stored my mint in a paper bag in the pantry. Kept its smell for ages compared to leaving it out. Makes you wonder why we don't just keep all herbs in the dark, right?