I'm a proficient speaker of Mandarin Chinese, and this is the best advice I can give to a non-speaker:
Say the word "she" with your teeth almost together and your lower jaw extended just slightly; add a "yo" sound (as in: "Yo dawg, what up!") at the end. Say it as one syllable. Try to keep the syllable as short as possible.
As for the tone of the word, speak the word as if it were a stabbing motion in volume and emphasis; like a sharp, downward motion. Or, if you prefer, imagine the sound of a speeding car whooshing past in a cartoon. The volume starts loud and ends quiet.
My friend and I asked my Chinese teacher (Mandarin) and she confirmed our assumptions that it is pronounced she-oh she-oh. And that's with a quick 'sh' sound in the beginning. But it's not like it matters, since we've proven that in a relatively small group of assholes, we can come up with about 2435098234703426 different variations of a three letter word.
OK, beyond the pronunciation... but related. I more interested in the implications of the name for the band. One poster mentioned that the name of the band is from the Movie called "Tian Yu" or "Xiu Xiu, the sent down girl." If your still out there, do you know this for sure? I speak decent mandarin, and there are dozens of chinese characters (words) that are all romanized "xiu", includeing words meaning "beautiful" or "excellent" (from the main character fo the movie), "shame", "rest", "rust", etc, etc. I never thought of Polish before, but I guess that possible. However, the traditional chinese opera sounding percussion in several tracks on "promise" kind of lead me to believe that the root is china. Any more idea?
If the name is truly derived from the movie Xiu Xiu: The Sent Down Girl, then the "correct" pronunciation would be "she-yo she-yo" (kind of, you'd really have to take a Chinese class to know exactly how to say it.)
It does not change with other dialects. The way it is written in English uses the pinyin system of romanization, which is only used for Mandarin, which is a dialect. Other dialects would not say anything like this, because most other dialects of Chinese are as mutually unintelligible as English and German; that is, you'll hear a similarity here and there, but for the most part, you won't know what the hell is going on. A Cantonese speaker saying those words (given the characters) wouldn't say "shoo shoo" or "zoo zoo" or anything even close to like it. It might be said closer to one of those ways by a person with a different accent, for instance, a Taiwanese person, but the difference would be fairly slight and still essentially the same pronunciation.
I say this is "correct" because Jamie says "shoo shoo," and however the band says their name is pronounced is the way it is pronounced.