In part 1, subjects will receive bosutinib and capecitabine daily at different dose levels of each drug in order to determine the highest tolerated dose of the combination study treatment. In part 2, subjects will receive bosutinib and capecitabine at this highest tolerated dose to see how well the study treatment works to treat breast cancer. In addition, genetic research testing (research analyses involving genes and gene products) will be performed on biological samples from subjects.