What is is Biddy’s letter & how does Pip react to it?

Biddy's letter let Pip know that Joe would be visiting. Pip reacted poorly, hoping that no one would notice Joe's visit, as it embarrassed him. Pip didn't see Joe as the right kind of person to associate with in his new life.

I received this letter by the post on Monday morning, and therefore its appointment was for next day. Let me confess exactly with what feelings I looked forward to Joe’s coming.

Not with pleasure, though I was bound to him by so many ties; no; with considerable disturbance, some mortification, and a keen sense of incongruity. If I could have kept him away by paying money, I certainly would have paid money. My greatest reassurance was that he was coming to Barnard’s Inn, not to Hammersmith, and consequently would not fall in Bentley Drummle’s way. I had little objection to his being seen by Herbert or his father, for both of whom I had a respect; but I had the sharpest sensitiveness as to his being seen by Drummle, whom I held in contempt. So, throughout life, our worst weaknesses and meannesses are usually committed for the sake of the people whom we most despise.