I'm not sure what a bugbear is but that is grammatically correct. Your title and your edit are both grammatically correct but they mean different things. So it depends on what exactly you are trying to say. Are you trying to say that spiders are really big bugs, so they are like the bears of the bugs? If so I would probably word it as, "Spiders are the bears of the insect kingdom."

Also, who is the spider scaring? If it is scaring other bugs then 'for bugs' or 'to other bugs' is ok. If the spiders are scaring people you would say the spider is the bugbear (or boogie man) of bugs.