How To Convince Your Mom You Need A Bra?

I know how.
Ecause you've already had a problem talking about this with your mum, you're going need to be quite tactful about how you bring it up again. (I'm a mum myself now, so I'm thinking about this from her side as well as yours.) You need to sound really calm and mature about it, and ideally ask at a time when you've already been chatting nicely for a while - don't spring it on her out of the blue when
  she's busy, or something! If you avoid a whining tone of voice, and don't sound like a little kid begging for something, she's going to have to start taking you seriously.

You need to state the facts:
'At my age, most girls wear bras.
I need one because my breasts show through my clothes and boys stare at them. I feel like I'm on display but I want to be more modest.'

Telling her that you want to be more modest might help! She won't want to admit that her little girl is growing up, but she also won't want to think that her little girl looks sexy, so being honest about your discomfort around boys will probably help her to understand that you are serious about needing a bra.

I'll be thinking of you - best of luck!

Cry when you come home and tell her that guys are looking at your chest and telling other guys about it and making fun of you.