Can you lose weight without losing bust size?

In a word; yes. However this depends on individual physiology and how your body stores and loses fat. If you want to lose body fat and find your bust size diminishing, don't worry, your best bet is to get as much of your body to where you feel comfortable and perhaps try to develop your pectoral muscles (under your breasts) this will make them seem larger without invasive surgery.

Chat to someone at a gym who looks pretty toned up or better yet a trainer to find out ways to build your pectoralis major without building up your arms too much

Sorry if this isn't the answer you wanted.