ANDY'S ANSWER: If it were me, I would find a time when we had a private moment and say, "Dad, I think I have to go bra shopping. When can we do that?"
If you needed a bigger pair of shoes, I'm sure you would have no problem telling your Dad that. Your breasts getting larger are a natural part of you growing. Neither your Dad nor you should be embarrassed about it. If you treat it matter-of-factly, everyone will be more comfortable and more open about your changing needs, including your asking to start stocking feminine protection for your impending period.