We present transport measurements on high-mobility bilayer graphene fully encapsulated in hexagonal boron nitride. We show two terminal quantum Hall effect measurements which exhibit full symmetry broken Landau levels at low magnetic fields. From weak localization measurements, we extract gate-tunable phase-coherence times τϕ as well as the inter- and intravalley scattering times τi and τ*, respectively. While τϕ is in qualitative agreement with an electron-electron interaction-mediated dephasing mechanism, electron spin-flip scattering processes are limiting τϕ at low temperatures. The analysis of τi and τ* points to local strain fluctuation as the most probable mechanism for limiting the mobility in high-quality bilayer graphene.