To get rid of bulkiness in muscles you want to stretch them out.
If you were to look at most ballerina's arms they look quite slender.
As a result of what they do they're constantly stretching the muscles and not lifting anything with them except the weight of the arm.
Try standing and reach out in either direction with both arms.
You should feel the muscles stretching.
Reach up, forward, down etc.
You'll get the feel for it.
Try taking a ballet class.
Or for starters, go watch a class and notice the thin arms.