You could check to see whether the roots have blocked up the drainage holes and left the plants too wet. Generally they're 'cast iron plants' and difficult to kill.

We did have a lot more rain than plants have been used to, I suspect it is more that, and possibly they got water-logged and the roots are struggling a bit to breathe. As tropicbreezent suggests I'd check the drainage holes, esp for any signs of soil coming out which might indicate that worms have invaded looking for dryer ground, nothing surer to ruin pot drainage than a couple of fat worms.
The rather cold early start might have been a shock to their systems too. If you see new growth that's good, I'd be inclined to sacrifice the flowers for the sake of saving strength and tip prune them but not fertilize them until the end of winter or beginning of spring. Some extra minerals might be needed to counter-act any leaching of nutrients over the wetter times to green them up a bit but not too much as they are better starved a bit to help flowering.

Thanks to this topic. I have been searching for answers how to take care and maintain bougainvillea as it is my first time to plant them. I will apply the tips I've read here :)

If you've got a wheel barrow with a pneumatic (pump-up) wheel, be wary you don't run over those devilish bougainvillea thorns; I've never known anything, not even rose off-cuts, that'll puncture a tyre quicker.
Just a handy tip!