Nitjoe
I'm shy and like modest swimwear too. I love the bathing suits from LL Bean:
Swimwear: Women's at L.L.Bean
They're quite pricey but well worth it. The link above is to their sale swimwear items. I have their jogger skort, the tankini top, and skirted bottom. These items have really liberated me, especially on holiday, when you may not always be able to reach for a towel and cover up the nanosecond you get out of the water. I went snorkelling in the tankini and skirted bottom and felt very comfortable.
Their swimdress looks really good if you want to cover up even more. I recommend these items very highly.
Hope this solves your problem - swimming is great fun and good for you too!