The answer to 'cockroach bites' is that cockroaches do not typically bite humans. Cockroaches are omnivores and will sometimes nibble on human skin, but they do not have the mouthparts to actually bite and draw blood. The small marks or irritation that may appear are usually from the cockroach's mouth parts, not a true bite.
However, cockroach infestations can still be a serious problem for homeowners. Cockroaches can spread bacteria, contaminate food, and trigger allergic reactions or asthma attacks in some people. If you suspect a cockroach problem, it's best to take action quickly to eliminate the infestation before it gets out of control. This may require using professional pest control services, as cockroaches can be difficult to fully eradicate on your own.