Does taking a hot bath get rid of a cold?

No. If your body is trying to mount a fever to help eliminate the pathogens responsible for the cold, taking a bath will make it easier to reach a higher temperature, for a little while... but then your body will just have to make up for the difference when you get out of the bath anyway.

Baths are very relaxing, though, and anything that soothes your body and mind will help you deal with the stress of having a cold.