Yes you can apply for both BDS and MBBS courses using same neet ug score card as neet organises single councelling for both the courses. You can apply for counselling on following dates for both of the courses.

MCC will commence the registration for NEET 2019 counselling on June 19 till June 24, 2019. After that the process of choice filling for the first round of NEET counselling will start at that  time of choice filling you will get that chance to select either BDS or MBBS or both of the coures with their colleges in which you want to get admission. You have to select the name of colleges on the basis of your preference order. Dont forget to see last years trends which will help you in choice filling process. You have to give your choices based on your prefrance but you will get only one college ,that means only one seat in either MBBS or BDS based on your marks and prefrences

for further counselling process you can visit the link below