Bose-Einstein correlations between identified charged pions are measured for p+Pb collisions at root s(NN) = 5.02 TeV using data recorded by the ATLAS detector at the CERN Large Hadron Collider corresponding to a total integrated luminosity of 28 nb(-1). Pions are identified using ionization energy loss measured in the pixel detector. Two-particle correlation functions and the extracted source radii are presented as a function of collision centrality as well as the average transverse momentum (k(T)) and rapidity (y*(pi pi)) of the pair. Pairs are selected with a rapidity -2 < y*(pi pi) < 1 and with an average transverse momentum 0.1 < k(T) < 0.8 GeV. The effect of jet fragmentation on the two-particle correlation function is studied, and a ...