Without knowing the relationship though, it's hard to advise on what is an appropriate way of approaching the woman. Or whether it is even appropriate for you to do so!
I'm really not begging you to disclose here at all
, but just saying a if it was a niece you saw regularly (for example) you could have a different approach to say, a colleague that you are concerned about.
The woman may be perfectly happy, but it seems you think she isn't for some reason. I think instinct is usually fairly reliable, but again it depends on how well you actually know her.
If you are concerned enough, to want to approach her, I would just genuinely ask her if she is happy with her life? Perhaps if there is a shared family event like wedding or significant birthday, this may be a good "trigger" to start a one to one, initially "general" conversation without seeming to pry. I would also ask yourself though not only why you want to know if she is happy, but what if anything you could do about it anyway.
If you do want to have the conversation and regularly travel in a car with said person, as PP said, this is a good way to have a low key conversation which a lot of people find comfortable as there is no direct eye contact. Or cooking something together.
It's difficult as she may be genuinely happy and/ or very private and your relationship with her could mean you might be prying or unnecessarily intrusive. There might be something she isn't comfortable sharing eg a married lover or (more likely maybe) a girlfriend.
It's tricky to advise you though as (being very honest) if she is in her 30s and hasn't seen fit to confide or discuss her feelings with you until now, she may just not want to. I don't see the harm though in saying to someone you care about "I am a little worried about you, is everything ok?" And leave it very general rather than saying what you have in your op eg "you don't have any social life" 