Answer:
Given the strenuous dance style, there are several options. One is the classic "bowl" or "pixie" cut. This style is versatile, yet will not whip your partner during one of the tighter holds. It can be very flattering, yet will keep the face free without the danger of the hair obscuring the face during the dance.
If you do not fancy a short hairstyle, the traditional bun is done for a specific reason. It is tight, keeps the hair in place, and does not let it flow. The flowing hair can be a definite hazard because of the possibility of "blinding" your partner during the sudden stops and lifts. Gravity will win in any hairstyle, so this is the prime consideration.
Another alternative is the French twist. It has the same purpose as the bun, but is equally tight. The advantage to this style is that one can use more accessories in the hair for effect as there is a longer line at the twist to use. Feathers or rhinestone clips and combs are effective for decoration.
Speak with other dancers...and your partner...about which hairstyle works best for you.