One way to dry a wedding bouquet is to hang the bouquet upside down as soon as you can after the wedding. This helps the flowers to keep their original shape as they air-dry. The air-drying process will take a while, so it could take a month for them to dry.
Spraying them with hair spray immediately following the wedding before hanging them upside down, creates a sort of layer of protection around the petals and can shield the flowers from losing their original shape.
There are companies that freeze-dry wedding bouquets which will keep it looking on-the-day-fresh for decades to come.
Here’s a UK company that offers freeze-drying bouquet preserving, wholesale freeze-dried rose petals for confetti and pre-freeze dried bouquets which some brides use for destination weddings: