Mouche, a disclaimer first: I have some opinions, but not much actual experience. That said, there are degrees in dom/sub relationships that matter a lot. If a girl gets off on being told what to do, rather than being asked: turn around, bend over, suck my cock, etc. That could be the level of naturally obedience that she's looking for. And I personally would enjoy that. But kinkier dom/sub relationships go much further along the spectrum. They will involve intentionally degrading the girl, handling her roughly and with disrespect, even intentionally causing pain. No judgement! If it's consensual and that floats your boats, party on! I would try to find out what her actual fantasy about being obedient entails.
As noted by the other responses, being submissive can mean different things to different women.
For some, it means they just don't want to have to make decisions on anything from where to eat to, well "what to eat" :p so to speak. They want a man to take charge; it makes them feel safe and valued.
For others, submissive is a cover term that translates to a desire to be dominated. That could include giving physical directions for sexual acts all the way to more forceful actions by you, to degrading/humiliating role play, to rough-sex actions like slapping, spanking, choking, hair pulling, restraints, and in rare cases even causing some level of pain or leaving marks.
I've had a few SB's that lean into the role play and physical stuff up to a limit. That limit was always discussed in advance, at the start of every BCD session. It is, as always, about mutual consent. You must ask and ensure you understand limits before you start playing. I've had a few sessions where she wanted much more than I was comfortable doing. I don't want to leave marks, cause bleeding, wrench muscles, or create phycological trauma. Plus, sometimes I just want a long, slow, deep BJ while I admire her ass. LOL I will return the favor, of course.
A good way to start the pre-sex discussion is to ask her about what happened with a past partner that she really wants to repeat. Then there's the usual safety stuff; establish a safe word and safe gesture, agree on a few "check in" spots periodically so she can take a breath and reconfirm all is good to continue. And very important, especially after a lot of hard role-playing, an after-care action like gentle hugs, soothing words of affection, offering a towel or water, etc. That affection serves as a balance to the more intense moments.
Interestingly, both of my current Porn Stars are into some level of this. With the Asian PS, I've been asked to slap her face and choke her harder, spank until her ass glows red, and more. I was concerned at first that she was just doing what she thought I wanted based on some of her more intense kink scenes. But after a bit more clarification and based on how wet she got begging me to choke her, I stepped it up to my limit, but no further. I'll admit, I can get into it, but it's not my primary method of deriving pleasure.
My advice: At the appropriate time, ask her what turns her on, specifically. Then align your comfort levels and boundaries with her and enjoy the fantasy.
Life is good
The Cat