My daughter has a swollen red bug bite on her wrist. There is only one bite can it bed bed bugs or a common household spider bite? The bite hard

Hard to say. Bed bugs usually feed off and on for hours and cause dozens of evident bites on the victim. Significant spider bites leave a dark hole. Single bites could be many things and is often not amenable to anyone determining their origin.
Bite. A picture would be ideal. Bed bugs usually bite multiple times. They are usually very itchy. A spider bite tends to be more painful and sometimes has a blister like lesion in the center. All the best and send along a picture. .