Recently, it has been observed that thin ferromagnetic Fe films deposited on top of (Ga,Mn)As layers induce a significant proximity polarization in the (Ga,Mn) As film even at room temperature. Furthermore, it was found that a thin interfacial region of the (Ga,Mn) As film is coupled antiferromagnetically to the Fe layer. Here we report a series of combined x-ray magnetic dichroism and superconducting quantum interference device magnetometer measurements for Fe/(Ga,Mn) As bilayers where the (Ga,Mn) As layer thickness is varied between 5 and 50 nm. We find a reorientation transition of the magnetic proximity polarization as a function of the (Ga,Mn) As thickness. The data are compared to results obtained performing ab initio calculations. A varying concentration of Mn interstitials as a function of (Ga,Mn) As layer thickness is responsible for this reorientation. Furthermore, exchange bias is studied in the fully epitaxial bilayer system. We find a rather strong ferromagnetic exchange bias. The strength of the exchange bias can be estimated by using a simple partial domain wall model.