Choose a bookmark on the map, tap it and then tap “Share” button in the place page. To share all bookmarks in a list at once, tap the double star symbol on the main screen, tap the icon with three dots in front of name of the list with bookmarks and tap "Export file" in the pop-up window.
Note: some app or services may not support bookmark .KMZ format. In such case if you share bookmarks via "Export file" option, only a link will be sent without bookmark file itself. You will be able to import bookmarks back if the file is attached to the link.
See also: How to enable auto backup for bookmarks?