Was stuck there too.
To start the beach date: you need to be at 20 LP, on summer, weekend, between 14:00-16:00 o´clock, need to have atleast a bike and you have to call her on phone and ask for a date!
Her next date is quite specific too. You don't have to take her to a cinema date instead you have to meet her when shes at the cinema on her own and than there will be a new "invite to date"-icon for her.