This is an interesting question. I was just hired to an assistant professor position for which the desired specialty was computational social science, so I may have some relevant perspective. My field is communication, a field which sometimes describes itself as part of the humanities but is better described as a social science with a strong professional orientation as well.
First, I should note that your question does not make it clear what kind of career you would like to pursue after you get your PhD (if you choose to get one). I will answer this question as if you prefer an academic career (i.e., you would like to be a professor).
With this in mind, I should note that professors in computer science departments earn much more money than in the social sciences. According to this, the median assistant professor in CS earns $107,000. Assistant professors in the social sciences appear to earn a median of $63,000 (but do note these are two separate sources). Based on what I know about the field of communication, I'd be surprised if there are any newly-hired assistant professors making $100,000, at least outside of a few places like the state of California where such a salary doesn't go nearly as far.
That being said, you should of course not study CS or in any other discipline if you do not like it. The ultimate reward of a PhD is, in my and many others' opinions, not worth suffering for 4-7 years to get the degree. If you like what you're studying, and find the typically low pay such students get tolerable, then it can be quite rewarding.
I think most quantitative social science fields have growing interest in computational social science. In communication, there certainly is, thanks in part to the existence of so much widely available data that constitutes communication (tweets, news archives, etc.). Training in this area would require initiative on the part of the student — few graduate programs have a formal program available. The best thing to do would be to find programs with more than one computational social scientists on their faculty (more than one makes it more likely you have some "in-house" courses and protects you from having an important faculty member leave you with no adviser).
One thing you may enjoy is that your background in computer science could give you a significant advantage over your social science peers in terms of technical skill. Most computational social scientists in the field are like me, people who self-trained their computational skills in an ad hoc way. You will surely have technical skills to learn but you should have a much easier time picking these things up. You will find at many programs that a significant portion of students are at least mildly repulsed by scientific computing — they think highly of those with skills, but see it as too challenging to attempt themselves. Among senior faculty, this attitude is even more prevalent.
Clever students with CS background could bring insights and skills from CS that wouldn't be particularly novel to computer scientists but might be very useful and otherwise unavailable to people in the social sciences. You might also be able to better comprehend new developments in CS while most other social scientists wait for these innovations to be better explained to non-experts (and perhaps wait for a C or some other less accessible implementation to be moved to Python/R or whatever).
Of course, the challenge in terms of curriculum will be a lack of background in the subject matter. I can't speak for political science, for instance, but my field regularly recruits people with no background in the subject area to its graduate programs. I only had a humanities background paired with some self-study in preparation for grad school when I started my PhD. I like to think that you do not have to be a genius or extensively trained to become a competent social scientist over the course of a PhD program as long as you are willing to work hard, know how to write/communicate, and are comfortable with abstract and empathetic thinking about the social world.
Just to boost my own field for a moment, here's why you might consider a degree in communication:
Although communication is not a high-paying field as far as professors are concerned, it has a much healthier academic job market than virtually any other humanities or social science field. One easy metric to consider is this: There are more faculty job openings each year than there are new PhDs. I expect faculty hiring to continue to increase because the discipline is very popular among undergraduates (for good reason).
If you have broad interest in social science and want the freedom to study topics that are interesting to you and other people might find interesting too, I think you may find a home in communication. The example you gave about examining gender bias through language is certainly a thing communication scientists do (but linguists and surely some others do as well). I was attracted to the field in part because so many different subjects can fall under the broad umbrella of communication — politics, social relationships, child development, information technology, public health, and many more things.
The field is notoriously open to outside perspectives, particularly when it comes to methodology. This is partly why it has been so accepting of computational social science and why so many job ads explicitly target these skills. The field isn't terribly tool-oriented; there aren't constant battles over the best methods of analysis like are common in economics and political science. So if you want to use the toolbox of computer science but don't want your days to be occupied with minutiae of algorithms, communication is a discipline that's quite open to this. I don't want to say the field doesn't care about rigor — in fact a journal was just founded to help develop and refine computational methods — but there will always be a demand that your method not just be sound, but also that it should teach us something about the social world.
Other fields of interest: information science is one you didn't mention but they are trying to develop these skills and want to become the home of data science on college campuses. Sociology is good, especially if you want to do social network analysis (the statistical methods, not necessarily studying Facebook, etc.), but a very difficult job market. Economics pays well but it's a difficult job market, hard to get into without prior economics training, and economists are not big fans of non-econometric methods (speaking very broadly). Based on what I know, if there are data science PhD programs I wouldn't bother with them and would rather prefer applied statistics or sticking to a social science field.
