By continuously scanning a femtosecond laser beam across a fused silica specimen, we demonstrate the formation of self-organized bubbles buried in the material. Rather than using high intensity pulses and high numerical aperture to induce explosions in the material, here bubbles form as a consequence of cumulative energy deposits. We observe a transition between chaotic and self-organized patterns at high scanning rate (above 10 mm/s). Through modeling the energy exchange, we outline the similarities of this phenomenon with other non-linear dynamical systems. Furthermore, we demonstrate with this method the high-speed writing of two- and three- dimensional bubble "crystals" in bulk silica.