Does spider bites spread?

Not usually. If you are bitten by brown recluse spider bite then the black area can spread. A severe reaction to any arthropod bite can spread.
Brown recluse. Brown recluse spider's bite can cause no reaction, a mild reaction, an immediate or a delayed reaction. With a significant reaction a which blister appears after bit. The surrounding skin becomes hard, swollen & can be red, white & blue. A deep lesion can develop which can eat through fat and muscle.