The production and semi-leptonic decay of heavy quarks have been studied in the photoproduction process e+p → e+ + dijet + e- + X with the ZEUS detector at HERA using an integrated luminosity of 38.5 pb-1. Events with photon-proton centre-of-mass energies, Wγp, between 134 and 269 GeV and a photon virtuality, Q2, less than 1 GeV2 were selected requiring at least two jets of transverse energy Ejet1(2)T > 7(6) GeV and an electron in the final state. The electrons were identified by employing the ionisation energy loss measurement. The contribution of beauty quarks was determined using the transverse momentum of the electron relative to the axis of the closest jet, prelT. The data, after background subtraction, were fit with a Monte Carlo simulation including beauty and charm decays. The measured beauty cross section was extrapolated to the parton level with the b quark restricted to the region of transverse momentum pbT > = 5 GeV and pseudorapidity |ηb| < 2. The extrapolated cross section is 1.6 ± 0.4 (stat.)+0.3-0.5(syst.)+0.2-0.4(ext.) nb. The result is compared to a perturbative QCD calculation performed to next-to-leading order.