This really depends on how you define bugs, and I keep seing different definitions. The most restrictive one: Just the infra-order hemiptera (insects that generally have two pairs of wings, with the anterior wings covering the posterior wings while overlapping with each-other a bit... But some of them lost their wings altogether, like fire bugs). That includes stinkbugs, cicadas, and aphids but excludes other infra-orders of insects (butterflies, wasps, beetles, grasshoppers,flies...)

A broader definition is simply synonimous with insects.

Then, many definitions are polyphyletic (which means some bugs may be more cloaely related to some none-bugs than to each-other). A common one could be "land arthropods" and would include insects, arachnids, myriapods and isopods (which are crustaceans) but that'd still exclude limules, which are mostly aquatic. That would, however, now include some species of hermit crab and not others, which is too counterintuitive, so maybe explicitly ban decapod crustaceans from being bugs? Then again, I saw people refer to shrimps as bugs, and they're also decapods. You could add a size constraints, but the smallest crabs are smaller than the biggest true bugs (even by the narrowest definition).

Then, you could drop the "land" constraint and go back to a monophyletic definition by making it synonimous with arthropod. That definition would finally include limules.

But then, so are crabs, so are sea-spiders, and so are all the extinct guys like trilobites (which are more related to myriapods, crustaceans and insects), eurypterids (aka sea scorpions, more related to limules and arachnids) and radiodonts anomalocaris (less related to extant arthropods than they are to each-others).

Ok, maybe we can exclude radiodonts by taking the crown arthropod group. But triolobites and eurypterids must definetely stay!

By this broader definition (whether or not you keep radiodonts in it), the biggest bug ever known to have existed would've been jaekelopterus, one of the eurypterids, at 2.5 meters long!