Choose a bookmark on the map and tap “Share”. To share all bookmarks in set at once, tap star symbol on the main screen panel, choose a set and tap "Share” button. Choose how you would like to share it.
Alternatively, you can copy kml files from MapsWithMe folder (it's stored in the root of the internal memory). You can use almost any file manager. Some file managers like Samsung file manager can't read .kml or .kmz files, but you can use other file managers, for example, Total Commander.
Choose a bookmark on the map and tap “Share”. To share all bookmarks in set at once, tap star symbol on the main screen, choose a set and tap "Share by email"* and send to yourself or to your friends.
You can also save bookmarks to any cloud service: send email to yourself, tap and hold kmz file and choose cloud service, for example, iCloud (Save Attachment), Google Drive, Dropbox, etc. You can also use AirDrop to share the file across your devices.
If you don't see "Share by email" button, please check iOS Settings – Mail – Accounts – log in with your account (iCloud, Gmail, etc.) and enable synchronisation with Mail app.
Alternatively, you can copy bookmarks (kml files, for example My Places.kml) directly from the app's folder.