How can I get the bones in my neck/chest area to protrude like ballerinas.?

You need to aim for a body that is healthy for you and also looks good for ballet if you want to become a ballet dancer. If you do not want to become a dancer or go into a profession where weight is important, then anything related to weight should not matter as long as you are healthy. If there was a problem with weight a teacher or another member of staff would have addressed it with you. There is a book called 'Diet for Dancers' you can use as a guide to maintain the weight required for a ballet dancer while having enough energy to dance, but be careful not to go to extremes.

Extreme thinness is not beautifully thin. Having bones protrude excessively is not a sign of beauty, but of sickness. There is a point of being too thin, even for a ballet dancer. If you eat nothing like the other answer suggested, you will slow your metabolism and lose muscle, therefore losing the look needed for a ballet dancer. You need muscle or you can't dance.

Eat healthy and drink plenty of water. Little and often is usually better for a dancer, but this may not apply to all. Make sure you get the right proportions of food groups and eat enough to maintain energy for daily life, school and dance but do not overeat.

Striving for this by starving or severely restricting your food intake can be dangerous. If you lose too much weight your dance school won't let you keep taking classes and may expel you. You can literally die from doing this, and if you go to extremes you will likely regret it.

If you are unfortunate enough to have a teacher tell you to 'stop eating' or to 'wish for anorexia' or something close (ridiculous things that should never be said and by no means apply to dancers or dance students), DO NOT take it seriously. You might not be allowed to dance if you don't eat enough, and wishing for anorexia is idiotic especially as it may lead to you being dismissed from school. If a teacher tells you to lose weight, you need to stop and think if you really need to. Teachers say all sorts of things and sometimes when it is uncalled for. If you really should lose the weight, then do so and do so properly. But if you are thin enough already and/or if it is not possible to lose weight without hurting your health, think twice and don't make a decision that should not be made.

If no one has said anything, you don't need to lose weight or do anything to achieve this 'look' anyway.

Stop eating.