JOEL - Church standards regarding how we dress are based on modesty. Members who are modest are always aware of current standards of taste and decency. They know that within the bounds the Lord has established, norms of modesty may vary from culture to culture, from generation to generation, from youth to aged, and even from one activity to another. When it comes to the activity of swimming Church leaders have discouraged the wearing of bikinis. President David O. Mckay said,

“Any bathing suit which immodestly exposes the body, such as bikinis or those with bare midriffs, etc., should not be worn. Swim suits are fashioned for a particular purpose and should not be worn as casual dress for summer, but should be worn only for swimming. While traveling to and from the beach or swimming pools, young men and women should be fully dressed, or at least their swimming suits should be covered with outer clothing.” (For the Strength of Youth pamphlet)

The following statement on women’s and girls’ dress was recently approved by the First Presidency and the Council of the Twelve:

“… We have always counseled our members to be modest in their dress, maintaining such standards in connection therewith as would not be embarrassing to themselves and to their relatives, friends, and associates."

BYU students must follow the Dress and Grooming Standards of the university which states:
"Clothing including swimming suits must be modest in fabric, fit, and style (no bikini, two-piece, or French-cut styles)." (1998-99 BYU General Catalog)
The over-riding principle in all this is one of modesty. But it can not all be spelled out for us. It is up to the individual to make an honest decision about which particular piece of clothing is modest and which is not. However, the direction from the church leaders does seem clear when it comes to bikinis.