When my sister was pregnant with her baby she was having a hard time with labor and the baby was getting late to come out.
So someone suggested she take a hot bath and relax in the bath and I guess it was true as after a few hot baths she finally went into labor and gave birth to a healthy baby boy.
So I would say that the hot bath can and does help to induce labor for some woman although you might have to take a few hot baths before the labor is induced.
The hot bath helps to relax your muscles and relax yourself as well and reduces stress so that can help with the labor to induce.
Stimulating your nipples and also having sexual intercourse during pregnancy can also sometimes help to induce the labor and get the baby to be born.
Exercise is also another way of helping to induce labor and to help keep you active and healthy.