My answer is in the following song parody:

I believe it was "M*A*S*H" Guerilla My Dreams (1979): Hawkeye refuses to accept a South Korean officer's warning that a wounded civilian woman he brought in is a dangerous enemy guerrilla soldier. (http://imdb.com/title/tt0638319/) Hawkeye refers to the Korean Officer as a "son of a bitch" when he realizes they just healed this woman only so she can be tortured for information.That's when I first remember ever hearing it and it was such a shock! Dynasty ran from 1981 - 1989 and The verbal spars between Krystle and Alexis also marked one of the first times the word "bitch" was used on US television. (http://en.wikipedia.org/wiki/Dynasty_(TV_series)#Krystle_and_Alexis)

The first time I remember hearing the word was on Saturday Night Live in 1977. It came out of the mouth of Gilda Radner as Emily Litella to Jane Curtain on Weekend Update. So I found a transcript: 1/22/1977 Jane Curtin: You're very irresponsible, Miss Litella, and, as a matter of fact, if it were up to me, you wouldn't have this job right now. you're not fit to be a newscaster. Emily Litella: Oh, dear, well.. there's no reason to be so upset. I mean, you seem very cranky tonight. Is it that time, dear? Jane Curtin: No, it is not! And, if it was, it would be done of your business, anyway! [ pause ] Miss Litella, I think we've spent enough airtime with this issue, and I just think that, from now on, you should try to do your best, okay? Emily Litella: Oh, yes, dear, I'm very, very sorry, and I promise from now on that I will do my best. Jane Curtin: See that you do. Emily Litella: Bitch. Jane Curtin: Well, that's the news. Good night, and have a pleasant tomorrow. And again on 3/12/1977: Jane Curtin: It's wearing thin, Emily. Emily Litella: What is? Jane Curtin: The "Never mind" thing. You've been doing it for close to two years. At first it was cute, then it was tolerable; now it's annoying. Emily Litella: Oh, I'm sorry that you feel that way. Jane Curtin: You're ruining "Update"'s responsibility as a credible journalist. Emily Litella: Oh, my goodness, I -- Miss Curtin, I wouldn't want to do anything like that. Jane Curtin: I'm sure you wouldn't. [ smiles maliciously ] So, why don't you just quit "Update" and try your hand at something else? We can get along fine without you! Emily Litella: Perhaps you could -- bitch! Jane Curtin: [ stung once more, faces the camera ] That's our news for tonight. Good night, and have a pleasant tomorrow.