If I was interested in someone I would find a way to tell them. As long as, they are not married or involved with someone already. Ideally, as long as I can already take care of myself financially, and they are also living a life that is on track. (Neither person needs to be "rich" but personally I'd like to think we each could support ourselves productively and care for our own basic needs around the old homestead...no pun intended.) I can't say I'm "up on" what rules may exist in the Mormon church with regards to what is considered acceptable behavior from women, for this sort of circumstance. But, this is what I normally would do and think.

Here is a google that provides a lot of different links that might more specifically address your question. http://www.google.com/search?q=how+should+a+Mormon+woman+behave%3F&ie=utf-8&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a

I know this is an old question, but I’m just seeing it…. As an active Latter-day Saint, I don’t see any problem with this at all. I know several couples that met while one of them—then a full-time missionary—was teaching Christ’s Gospel to the other. In one ward, the missionary that had taught the now–elders quorum president was now his wife; in another, a missionary returned to an area he had served in and eventually married a woman he had met while serving there. If the two of you click, that’s great. Once he’s off his mission, he’s theoretically “fair game.” Now, that having been said, it is completely inappropriate for a missionary to be dating, flirting, courting, etc. *while* serving a mission. When I was a full-time missionary, I had a companion that quite obviously reciprocated the attention given him by a certain young woman in the branch. I won’t go into details, but suffice to say that certain mission rules were broken as the relationship progressed. I don’t think that either of them committed any serious sins (thank goodness), but a full-time mission is *not* the time to pursue a romantic relationship; it’s a time to serve the Lord and Him alone. (From your question, it’s obvious that you know this; I just wanted to clarify, for anyone else that might happen along.) Hope that still helps!