Is it true that I should avoid baths while pregnant?

NO. Bathing is fine while pregnant. You may however want to avoid public baths and jacuzzi/hottubs, etc.
No. You should avoid hot tubs and jacuzzis in pregnancy because the heat can cause birth defects in the baby's back. It is usually okay to take a bath in your bathtub if the water is warm (body temperature or less.) your blood pressure may drop making you dizzy when you stand up however so be very careful when getting in and out of the bathtub.