I would say a mixture of both, that is how it is with msot of these things. When it comes to being born with it - I would suggest a genetic tendency towards being submissive and perhaps a tendency of a sexual reaction with it. However, there are plenty of vanilla couples who do a little bit of D/s activities and also plenty of submissive people who don't derive pleasure from it.
Environment can effect it in a number of ways. Get locked in a tight space as a child and you could develop claustrophobia - or it could be something you enjoyed. This could develop into an interest in bondage. Particularly strict parents could mean that you end up looking for dominant characters. Or maybe in later life - a partner who is dominant in an entirely vanilla way could cause you to search for in later relationships, perhaps becoming more sexual.
Also, what exposure do you have to it. When I was a child I read books that in an entirely none sexual way had maltreatment in them. Nothing unsuitable for my age, but things that could feed into BDSM. I have now become a denzien of the internet and come across all manner of fetishes. In particular, before I joined here I was still a member of an adult baby/diaper lover site. It was talking to some subs on that site that reawakened my own subbie feelings that I had sort of lost once I went into puberty. Less contact with the concepts may stop something like this developing.
I would say there is a genetic tendancy, but a particular environment is required for it too occur, and with a particularly strong 'sub encouraging environment' someone might become a sub to some degree, even without the genetic tendancy.
On a personal note, as an adult baby I enjoyed some things that would be considered submissive or humiliating before I considered myself into BDSM. While the pleasure I derive from it is emotional and relaxing, not sexual, it is also possible that the nature of it itself led me to developing a 'sexual counterpart' to this emotional non sexual part of me.