go/come

I wonder if there is any difference between “1” and “2”.

  1. I’m going to Bill’s party tonight. Do you want to go with me?
  2. I’m going to Bill’s party tonight. Do you want to come with me?

There is little difference. “come” feels slightly more intimate.

More intimate with whom? Bill or the person he/she was taking to?
If the answer is Bill, does sentence #1 have opposite connotation, i.e. to suggest that the person he/she is talking to is more intimate?

More intimate between the speaker and the person he/she is inviting.