Try being more dominant on dates (speak up/fondle them in the movie theater, pay for dates, be the one moving them around and controlling the action during sex, find them in the evening and flirt dominantly if your skill is high enough, etc) and eventually a submission meter will appear under their romance stat.
It definitely could take a while! It took me a couple months ingame time to get a Master, for example. I think it goes faster if they have a naturally submissive personality (shy/insecure/passive people are more likely to be your sub then forward/aggressive/confident people) and of course they need the Submissive or Switch inclination.
A Dom/Sub relationship IS a romantic relationship, just with added mechanics. So if you're in a monogamous relationship (with a boyfriend/girlfriend or open partner) you can't also have a sub. But if you have the polyamorous inclination you can have as many poly partners and doms/subs as you want. You get the polyamorous inclination by starting with it, completing the Best Friend questline and choosing to be poly with them, or by cheating and giving yourself the inclination.