My first reaction is to not make her self conscious of her body. She is developing breasts, that's normal. Please don't make her feel negative about her body. She is developing body image now, if parents or friends are negative toward that, it sets off possible issues for later.
Communicate with her. We are open minded here and we talk about everything. Sometimes we do lounge around the house with no bra, we love and enbrace our bodies.
If she does not want to wear a bra, layer tank tops. My 15 yr old layers her tanks all the time with her bra. The athletic bra is another good option if you feel she should be so covered at all times.
I'm not saying go show the tatas off, of course modesty is important. There has to be a balance.
I didn't mean to come across the wrong way. I hope you interpreted my comment positively. Our girls grow up so fast!!