We carried out ac magnetic susceptibility measurements and muon spin relaxation spectroscopy on the cubic double perovskite Ba2YMoO6, down to 50 mK. Below similar to 1 K the muon relaxation is typical of a magnetic insulator with a spin-liquid type ground state, i.e. without broken symmetries or frozen moments. However, the ac susceptibility revealed a dilute-spin-glass-like transition below similar to 1 K. Antiferromagnetically coupled Mo5+ 4d(1) electrons in triply degenerate t(2g) orbitals are in this material arranged in a geometrically frustrated fcc lattice. Bulk magnetic susceptibility data has previously been interpreted in terms of a freezing to a heterogeneous state with non-magnetic sites where 4d(1) electrons have paired in spin-singlets dimers, and residual unpaired Mo5+ 4d(1) electron spins. Based on the magnetic heat capacity data it has been suggested that this heterogeneity is the result of kinetic constraints intrinsic to the physics of the pure system (possibly due to topological overprotection) leading to a self-induced glass of valence bonds between neighbouring 4d(1) electrons. The muon spin relaxation (mu SR) unambiguously points to a heterogeneous state with a static arrangement of unpaired electrons in a background of (valence bond) dimers between the majority of Mo5+ 4d electrons. The ac susceptibility data indicate that the residual magnetic moments freeze into a dilute-spin-glass-like state. This is in apparent contradiction with the muon-spin decoupling at 50 mK in fields up to 200 mT, which indicates that, remarkably, the time scale of the field fluctuations from the residual moments is similar to 5 ns. Comparable behaviour has been observed in other geometrically frustrated magnets with spin-liquid-like behaviour and the implications of our observations on Ba2YMoO6 are discussed in this context.