Would someone please explain me in which context I'd use the phrasal verb bugged out?
I've heard this expression once, but I couldn't understand its meaning as it seemed out of context.
There are two contexts for this. The first is when "eyes bug out", which is in reference to how many insect's eyes are large and bulbous. This essentially means the person was surprised or fearful and went wide-eyed.
The second context is a colloquialism, meaning "to leave quickly". If you say "He bugged right on out of there" it means that someone left extremely quickly, usually without making proper arrangements for other matters. If it's in the context of a bar with friends, he might not have said goodbye to them as is usually socially expected. If it's in the context of a devastating storm coming, it means that he didn't do much to secure his home or belongings, usually only taking necessities and instead prioritizing his own survival first.
This final case, that of the storm, is actually directly related to the term "bug out bag" which is a disaster preparedness bag, usually a duffel bag, stocked with a supply of water, shelf-stable food rations, first aid supplies, fire starter, some form of illumination, additional clothes, a knife, etc. Basically the minimum needed to survive in the event of an emergency where you have limited time to prepare for departure and your life depends on it.