Surface damage on fused silica optics initiated by high fluence 351 nm laser is one of the major bottlenecks for the high power laser systems, such as, Shenguang Ⅲ (SG-Ⅲ) laser facility. Generally, the CO2 laser, which is strongly absorbed by fused silica and thus can effectively heat fused silica above melting temperature, is used to locally mitigate the damages, called the non-evaporative mitigation method. However, subsurface bubbles may be introduced in the damage mitigation process by CO2 laser melting. Unfortunately, the mitigated damage sites with subsurface bubbles can be easily re-initiated upon subsequent laser shots. In this article, in order to eliminate the subsurface bubbles, we systematically investigate the influences of mitigation protocols in different ways of laser irradiation preheating on the formation and control of subsurface bubbles. Based on the simulated results of the temperature distribution and structural changes under CO2 laser irradiation, two CO2 laser-based non-evaporative mitigation methods are proposed, which are adopted for the mitigation of surface damage sites ranging in size from 150 m to 250 m, and systematically investigated to assess the effect of eliminating subsurface bubbles. The process of mitigation method I is that multiple laser irradiations with short time and increasing power are initially used to preheat the damage site and then a higher power laser irradiation is adopted to mitigate the damage site. The process of mitigation method Ⅱ is that a long time, low power laser irradiation is first used to preheat the damage site and then a high power laser irradiation is adopted to mitigate the damage site. The detailed morphologies of the mitigation sites and subsurface bubbles produced by the two mitigation methods are measured by optical microscope with high magnification. A large number of small subsurface bubbles are observed in mitigation method I. While, less subsurface bubbles are observed in mitigation method Ⅱ. The statistical results indicate that among the thirty-four mitigated sites, only eight have no surface bubbles in method I. In contrast, among the fifty-four mitigated sites, forty-nine have no surface bubbles in mitigation method Ⅱ. The experimental results suggest that the formation probability of subsurface bubbles is effectively suppressed by the mitigation method Ⅱ. The mechanism of eliminating subsurface bubbles in the mitigation method Ⅱ is discussed based on the structural changes of the fused silica in the mitigation process. It is found that the fused silica is not melted by the long time, low power laser irradiation, which means that a long time preheating without melting could provide enough time to effectively reject air and impurities enwrapping in cracks, and thus reducing the formation probability of subsurface bubbles in the form of the crack closing due to rapid melting. With the mitigation method Ⅱ, the probability of mitigated sites without subsurface bubbles can reach 98%.