First of all congratulations in achieving such great marks.

360 is sufficient marks to fetch you a semi govt. or govt. BDS seat. You will colleges based on three counselling -

ALL INDIA COUNSELLING :

Your chances of getting a seat through all india is little less as usually cut off of all india ranges from 450-500.

If you belong to obc (non creamy) or sc /st , there are probalities of getting  the govt. or semi govt. colleges through all india counselling ,having much lesser fees structure and of greater value.

But if you are general ,you should apply for this and wait for the last counselling, you may get the seat. 

STATE LEVEL COUNSELLING :

govt colleges:

Here you are having high chances of getting a bds seat ,depending upon the state you belong and colleges in it ,

FOR EXAMPLE, if you belong to states such as west bengal, uttarakhand,maharashtra ,karanataka.. you may easily get the seat.

SEMI GOVT COLLEGES :

With 360 marks  you should definitely apply for the COMEDK colleges ( semi govt. colleges of karnataka ) fees structure is too low and value of colleges are too high because of their locations in cities such as bangalore, mangalore,etc 

Even the patients are in good number for your practice and experience.

I ll definitely advice you to apply for comedk colleges(http://kea.kar.nic.in/cet_2017.htm), i have provided you the official link of last year, kindly check it twicw a day for next information to be uploaded.

PRIVATE COLLEGES:

ALL INDIA (PRIVATE) DEEMED UNIVERSITIES: Apply for the same through main neet website .

there are also some private colleges ,having high value and fees structure is also comfortable, you shuold also apply for them such as :

MANIPAL UNIVERITY BDS (https://manipal.edu/mcods-manipal.html)

UP DENTAL COLLEGES ,they are also easy to get .Keep checking on their website for the info.

 I hope the information i have provided will help you a lot . All the best for you futute