Wouldn't it be more grammatically correct to say "hatzneya leches lifnei Elokecha" instead of "hatzneya leches im Elokecha"? One is modest before G-d, in G-d's presence -- what does it mean to be modest "with G-d"?
The Midrash (BaMidbar Rabbah 1:3) tells us that before there was an Ohel Moed G-d spoke to Moshe from a burning bush in Midyan, G-d spoke to Moshe in Egypt, G-d spoke to Moshe from Har Sinai. However, now that there was an Ohel Moed G-d spoke only privately from that tent to fulfill the ideal of "hatzneya leches".
A number of points can be learned from this Chazal:
1) The source for the concept of tzniyus is rooted in the idea of imitating G-d. Just as we learn elsewhere mah hu rachum af atah..., we must act with kindness and mercy because G-d acts in this manner, so too "hatzneya leches im Elokecha", act with modesty not just before G-d, but along with G-d, meaning imitate the tzanu'a behavior which G-d has demonstrated. G-d does not call a news conference and make sure it is carried on all the major networks to say what he wants to; G-d speaks from the privacy of the Ohel Moed to those who are invited to listen.
2) Tzniyus means privacy. Even speaking anthropomorphically, I don't think the Midrash means that G-d wore a skirt below the knees and a blouse down to the wrists. Modesty and privacy are not the same thing. A person's dress can meet all the technical details that halacha requires but he/she can be a very loud and flashy person.
3) The Midrash continues that the paradigm of tzniyus was Moshe, about whom it is written, "kol kvuda bas melech pnima". Moshe was literally raised by a "melech", as he was adopted by Pharoah's daughter, but many of the meforshim explain the appelation of "bas melech" to refer to Moshe's relationship with Torah or he was the melech and the Torah itself is the "bas melech". In any event, this is clear: Moshe Rabeinu obviously did not shun taking a public leadership role as a result of his tzniyus. Tzniyus should not be an excuse to deny worthy men or women a public position.
What exactly is tzniyus? Chazal tell us that Torah requires tzniyus (Sukkah 49). Maharal (Nesiv haTzniyus ch 1.) explains that this is so because Torah has a "madreiga pnimis", a "madreiga nisteres." Torah has depth. Every parsha and sugya is like the top of an iceberg that protrudes above the sea, providing just a hint of the vastness which lies below. A person who embodies tzniyus is a person of depth, a person who is defined not by their clothes or hat or by a sound-bite, but a person whose character remains hidden behind a concealing veil and not on public display. Just when you think you have the person buttonholed, you discover that there is a deeper more pnimiyus aspect to the person's whole personality that you had previously overlooked or not seen. That's a person who is tzanu'a.
If we deconstruct the way tzniyus is taught and emphasized in our society, it pretty much turns this entire idea on its head. Rather than emphasize depth and inner-meaning, the emphasis is placed on externals: skirt length, sleeve length, hat size/color, etc. Don't get me wrong -- some of these details are important and halachically crucial. But these details are just the superficial siman of what defines tzniyus. What is missing is the stress on tzniyus as pnimiyus. We need to cultivate depth of character, not just a superficial commitment to a particular mode of dress.