Would a dust mask protect me from asbestos fibres?

No, it will not adequately protect you from asbestos. For asbestos. you have to have at minimum a half face respirator with HEPA cartridges and you have to be trained to use it. If you are not trained, the respirator will not even be enough. In such a bunker, there are much bigger hazards than the asbestos. There could be toxic chemicals, explosives, or pesticides. You should stay out.