How were the roman baths in bath discovered?

Several. The smallest I saw in Italy were two rooms with two different baths, but the largest had 4-5 rooms. It just depended on who the bath was for. The wealthy had larger complexes for baths than...

Because they were open to the public! Romans didnt care about bathing in public, they worshiped there bodies in every way. They thouht that there bodies was a work of art!

The names of the baths are the frigidarium (cold), the tepidarium (warm) and the caldarium (hot).

The Latin for bath is "balineum" or "lavatrio", if referring to a mineral or a hot bath, it is "thermae".

there was one in almost every roman town and city