I don't think the pose-topless-for-a-scanner thing is ridiculous at all. You could even imagine the device being video-based, something you run on your laptop (which obviously doesn't actually upload or even record pictures of you). If you can stand topless in front of a fitter, you can stand topless in front of a device.
A less intense approach, though, would be doing a better job of statistical modeling women's breast shapes and how well different kinds of bras fit them. If you sell bras for a while and different women return different ones, you can start to build a sense of what customers' ideal fits are and refine what bra shapes and styles get sent to them. Whether that data can be accumulated fast enough to make the service useful is an open question, but it at least doesn't sound crazy.
A less intense approach, though, would be doing a better job of statistical modeling women's breast shapes and how well different kinds of bras fit them. If you sell bras for a while and different women return different ones, you can start to build a sense of what customers' ideal fits are and refine what bra shapes and styles get sent to them. Whether that data can be accumulated fast enough to make the service useful is an open question, but it at least doesn't sound crazy.