Your description is probably of a moth to be exact. Many moths can be found in bathrooms because at night these are the only house lights left on. Moths migrate to light and can be found in bathrooms as a result. They will flutter until they either starve or get burned on the light.
Those are not moths, even though they are attracted to light. They are actually a type of mosquito found exclusively in North America. They do not feast on human blood and usually go into hibernation during winter months.
