The rheology of particle-laden fluids with a yield stress, such as mud or crystal-rich magmas, controls the mobility of bubbles, both the size needed to overcome the yield stress and their rise speed. We experimentally measured the velocities of bubbles and rigid spheres in mud sampled from the Davis-Schrimpf mud volcanoes adjacent to the Salton Sea, Southern California. Combined with previous measurements in the polymer gel Carbopol, we obtained an empirical model for the drag coefficient and bounded the conditions under which bubbles overcome the yield stress. Yield stresses typical of mud and basaltic magmas with sub-mm particles can immobilize millimeter to centimeter sized bubbles. At Stromboli volcano, Italy, a vertical yield stress gradient in the shallow conduit may immobilize bubbles with diameter . 1 cm and hinder slug coalescence.