Biking is not particularly good at developing core strength or flexability but it is better than doing no excecise and an excellent way of fitting activity into your everyday routine. Try cycling to the pool and swimming.
You have to take care that you are riding in a stance that suits your stength and flexability. A good starting point is the touring position with your back straight and at about 45 degress. Racers may select a lower position. Casual riders go for a more upright one.

Beware of rifding with a bent back; the classic mistake is to place the bars too high and close then hunch the shoulder and bend the spine to get lower. Check out your stance in a shop window reflection.