Mrs. Bennet sees what she wants to see - she expects very much to hear from Mr. Bingley, so a mysterious letter arriving at Netherfield must be written by Mr. Bingley whether he actually matches the description Mr. Bennet gave of the author is of little importance to her - or rather under these circumstances she finds it apt to perceive him as stranger (it's all relative of course). I'm sure in a conversation with Mrs. Lucas she would insist that Mr. Bingley has become a good friend of the family already.