1) Ask someone for a drink.
2) Ask someone out for a drink.
3) I asked her for a drink.
4) I asked her to have a drink with me.
To me when you ask someone for a drink, you ask them to give you a drink.
This is the place to post questions and discussions on usage and style. The members of the Wordwizard Clubhouse will also often be able to help you to formulate that difficult letter.
End of topic.