A courteous approach
If they accept, perhaps you'll become friends, comrades, or rivals. If they refuse... don't take it personally. Perhaps their social circle is already too large for them; perhaps they wish to reserve some time for their Protégés.
[Becoming Acquainted with someone increases Influence by 1; when your Influence passes 90, you can no longer add Acquaintances until your social circle has been reduced in size.]
Your friend will receive:
<Friend Name> has invited you to accept their Calling Card: a polite overture to other social actions! Accept, and they'll become an Acquaintance.
<Friend Name> has accepted your Calling Card. You are now both Acquainted.
The price of fame
In your case, the price of fame is the bill for a five-course dinner at Dante's, not to mention the bribe you needed to arrange a table at short notice. If your lucky toady-to-be doesn't appreciate it, perhaps they need a good snubbing.
Your friend will receive: [Friend] has offered to buy you dinner at Dante's Grill, if you'll spend the evening flattering them! This will reduce your Wounds and Suspicion, and also give them some of your Making Waves...
Your friend will receive: You have dined with [Friend] at Dante's Grill. The service was faultless; the five-course meal of Surface stuffs, mouth-wateringly invigorating; the brass cutlery was comfortably warm.
You will receive: You have dined with [Friend] at Dante's Grill. The service was faultless; the five-course meal of Surface stuffs, delightful; the brass cutlery was comfortably warm. And they laughed at all your jokes.