That friendly call to the GC is important, and although I say I don't do sales, that is part of sales.
It helps to call the GC's estimator a few times before the bid to build a bit of a rapport, then its not a cold call after the bid and this guy has no clue who you are.
Be helpful, and positive and even if you don't get the job keep in mind you may be bidding this guy again so keep it friendly.
I have known some of the big GC estimators for many years, and you have to keep in mind they move around and even move up sometimes and it helps if they know who you are and that you are easy to work with.