Here're the categories you could argue the bot falls into. The point of the "that's what she said" is to point out when phrases sound like something a woman might have said in bed or during some sort of sexual activity, furthering the already staggeringly vast perception our society has of women as primarily sexual objects. It's not what I'd call "grossly" sexist, but if somebody's objecting to it, she absolutely has a reason to feel uncomfortable about it.
I disagree that the supervisor is necessary here. First off, that's making an appeal to authority and such appeals can be pretty irritating; second off, that's trying to solve the problem privately rather than in public space. By making this bot, Jessamyn says that her voice is as valuable as anybody else's voice. If somebody else wants to make a bot that makes crude sex jokes, she can make a bot that quotes notable women. And rather than making a bot that's irritating or one-note, it sounds like she made a bot that has a variety of colorful responses, to the point where one of her coworkers told her how much he appreciates it.
Remember that sexism is about the reinforcement of cultural stereotypes, rather than being just about gross bigotry or discrimination. What's sexist is that people assume, in a workplace, that jokes about what women say in bed are acceptable. Those jokes make me a little uncomfortable even in a casual environment; it's kind of gross that people are okay with them at work. The sexism isn't one person consciously thinking "Oh man let's women the butt of jokes about sex!", it's that women-as-sex-objects is such a pervasive trope that we don't notice it unless somebody like Jessamyn points it out to us.