Outer space isn't vacuum! so? Although classical law stated that speed of light is constant in vacuum, going to lesser in denser medium and zero in superatomic field. Condition of ideal vacuum is not satisfied by expanding space between galaxies!
In this case, you consider two frames; Earth on which bob resides and other Star-ship in which Alice is used to travel nearer to c. As per your statement that Alice viewing to the Earth since she herself moves with near to c with respect to earth. So, Alice finds that Earth is moving apart from...
Since Edwin Hubble proposed distant galaxies move apart from each other as spectra of each galaxy is shifted towards the red end. this created the law that universe is expanding exponentially since big bang. and these galaxies spectra are due to stretching of wavelength of light incident from...