If it someone you are familiar with you can say: vorresti bere qualcosa con me - means would you like to drink something with me or more formal verrebe bere qualcosa con me - means the same thing

is your question about italian? if it's general, i'll tell you that in spain to have a drink with someone is really a common thing and hardly you ask but just announce you are going to have one and some one always joins. (a coffee or something light, in a pause, in waiting, etc. if you refer to socializing with the opponent sex, normally, in discos, etc both parts hold a drink and the strategics is to see if the other wants to spend the time to consume the drink with you, specially men. sometimes men also try to buy women a drink (buy a drink sounds horrible in spain but it's correct english, we use invite) but this is look as a direct expectation of "results" so you norm,ally don't buy a drink for a girl unless you think there is some kind of feeling. how are things going in zambia. would like to have some chat for you to explain me about your country. bye.

Ti va di bere qualcosa? Ti andrebbe di bere qualcosa?