Bath & bathe

Bath
The verb bath is used (in British English) to mean 'wash oneself in a bath (tub)'.
Children have to be made to bath regularly.

The verb is rather formal, and is not used is American English; in an informal style, we usually say have a bath (British) or take a bath (British and American):
I'm feeling hot and sticky; I think I'll take a bath.

Bath can also be used with an object (in British English):
It's your turn to bath the baby. (US ...to bathe the baby.)

bathe (bathe - bathing - bathed)
Bathe (in British English) can mean 'swim for pleasure'. It is rather formal in this sense (and is not used like this in American English); in an informal style, we usually say have a swim, go for a swim, go swimming or just swim:
Let's go for a swim in the river.

In American English, bathe is commonly used to mean 'take a bath':
I always bathe before I go to bed.

Bathe can also be used (in both British and American English) with an object, to talk about putting water on a part of the body that hurts (for instance sore eyes):
Your eyes are very red-you ought to bathe them.

To lie in the sun is to sunbathe (*not sunbath).