I met my ex-girlfriend in Swing Class. Originally, we started off as friends. I was kinda interested in several other girls at the time and was playing multiple angles to steal time with them. One explained to me that she had far too many guys asking her out (or at least she felt that since she could never actually find a guy who wanted to be her friend), so I almost instantly gave up trying to make her my girlfriend, though I'd still like to hear from her right about now.
Anyway, I'd spent years of my life trying to force relationships, but when I just tried to be friends, the relationships basically built themselves.
Anyway, as for your question, Miriel's got the right idea. If it turns out this girl is still who you imagine her to be and you wait until another "chance encounter", you might not get one and might end up missing out. If you show up at her door for the sole purpose of asking her out, it might come off a bit strange. If for any reason (i.e. your own setup) the two of you end up at the same place (i.e. your place, her place, mutual friend, get together, etc.), jump at the chance to talk to her since all you want is to get to know her right now. Then casually mention getting together sometime and you won't need an excuse or chance encounter ever again.