That Quote Is From....

So the Shakespearean insult: "I do desire we may be better strangers" is from As You Like It, Act III, Scene 2. Here is a larger context of that quote:

 JAQUES. I thank you for your company; but, good faith, I had as
    lief have been myself alone.
  ORLANDO. And so had I; but yet, for fashion sake, I thank you too
    for your society.
  JAQUES. God buy you; let's meet as little as we can.
  ORLANDO. I do desire we may be better strangers.
  JAQUES. I pray you mar no more trees with writing love songs in
    their barks.
  ORLANDO. I pray you mar no more of my verses with reading them
    ill-favouredly.