Dear rozie: At this time, there simply has not been a method of screening that is as reliable as mammography. An ultrasound can be done, but this may miss things that a mammogram can pick up. One option is to make arrangements with your center to see if the examination can be completed in one visit, rather than any call backs. An MRI could technically be done but this is so non-specific that a mammographic correlation is necessary to make sure unnecessary biopsies are not done.
the main imaging alternative is MRI; it is quite useful for the breast. The main reason it's not done routinely for breast imaging is it's much more expensive and time-consuming than mammography. Ultrasound is another way to image the breast, but it's not really an alternative because it doesn't have the ability to find very small abnormalities the way mammogram or MRI do.