As fas as I know
St.Barts is the most popular Caribbean island for celebrities. The two-week period starting before Christmas until the New Year is the busiest and best time for seeing celebrities there. The whole St. Barts island turns into a big party. The climate will be around 80 degrees and this island attracts mega moguls and celebrities during this time.
Taking photgraphs with celebrities is depends on the celebrity wish, sometimes they allow and somtimes they don't.
If yo go there, just try your best!