As per Ayurveda, the bran in brown rice is very rough and dry, and not recommended for Vata type body. What to do in this case?

As per the Satvic food philosophy, it is not so. Brown rice is perfectly suited for Vata body type as well, as it is wholesome (contains the nutrition, and the natural oils present in the rice). It is simply the whole, pure form of rice, without refinement, as given by Nature. 

However, that being said, we'd like you to practise your own judgement. If you're a Vata body type, try consuming brown rice for 2-3 weeks, and if you feel dryness, constipation, or any other discomfort, you may discontinue it. It's important to listen to your body.