What an interesting inquiry you have decided to pursue with your question of what is the world's record for the smallest bikini.

According to Naked World Records, the smallest bikini that exists is from Double Take Micro Ware. They consider a bikini to be a piece of clothing that covers the "vital parts." It's a bit questionable to us if this bikini really covers much at all; however, we are not the ones who determine what the definition of a bikini is.
Determining the exact length, width, etc. of a bikini is a bit difficult, and the measurements for this bikini are not available. Second of all, it would depend upon what size you decide to order this little number in. Anyway, the strings go behind the neck, where it ties. However, in the front, you only have a tiny covering over the women's chest to cover the most private parts. The same standard applies for the lower half of the bikini. There are only very thin strings; however, they do cover what is considered the most private part.
We cannot imagine though that you would get away with wearing such a bikini on too many public beaches. Just because you choose to define nudity in a certain way does not mean that the law agrees with your interpretation.
There is another bikini claiming to be the "unofficial" smallest in the world. Quite honestly, all that this bikini entails are a few strings of fabric strategically placed on the body. They really do not cover any of the body at all; therefore, this makes it "unofficial."