Graphene bubbles are often formed when graphene and other layered two-dimensional materials are vertically stacked as van der Waals heterostructures. Here, we investigate how graphene bubbles and their related disorder impact the quantum transport behavior of graphene in the absence and presence of external magnetic fields. By combining experimental observations and numerical simulations, we find that the disorder induced by the graphene bubbles is mainly from p-type dopants and the charge transport in pristine graphene can be severely influenced by the presence of bubbles via long- and short-range scattering even with a small bubble-coverage of 2% and below. Upon bubble density increase, we observe an overall decrease in carrier mobility, and the appearance of a second Dirac point on the electron carrier side. At high magnetic fields, the disorder from graphene bubbles primarily impacts the quantization of the lowest Landau level, resulting in quantum Hall features associated with a new Dirac cone at high charge carrier density.