Within finite-range density-functional theory, we have addressed the photo-ejection of electrons hosted in 4He bubbles as a function of pressure at zero temperature. It is shown that, besides the 1s→1p and 1s→2p transitions that show up in the whole pressure range up to solidification, there is another transition to a loosely bound 3p state that disappears at a pressure P above 1.7 bar. Realistic predictions for the electron photo-ejection cross section are made using a model that has been proven to reproduce the experimental infrared absorption transitions as a function of pressure.