1)”the picture of you in A bikini” refers to a specific picture, which you have seen before, in which the person happens to be wearing a bikini.

2)”the picture of you in THE bikini” refers to a specific picture, which you have seen before, of the person in a specific bikini which is the main focus of your request.

Now, if it were 3)”A picture of you in A bikini”, then it refers to any picture of the person in a bikini. Likewise, 4)”A picture of you in THE bikini” refers to any picture in which the person is wearing the specific bikini.

Muzukashii desune. Ganbatte kudasai.

Articles in English have a lot of flexibility. In a lot of cases, either a or the are correct. Most students of English want a rule, but that’s not very helpful. Just remember the basic difference (“a” for something non-specific/not previously mentioned, “the” for something specfic/previously mentioned) and you’re fine.

“A” bikini is any two-piece she happens to have lying around and in this case we can safely assume your interest is not so much in the swimwear as in the body it adorns.

“A bikini” means that any bikini will do.