Hej Lilian!
I would say "vackra barn; vackre gosse" in stead of "snygga kille". Bambino (and the Turkish cocuk) means child (male child). "Snygga kille" is more like "handsome bloke".
Yes, I thought about that, but I had the feeling that it was just an affectionate way of addressing a guy. It seems to me that this is a romantic message. But I may be wrong...