British & American Usage: Bath and Bathe

A bath (also a bathtub in American English) is a large basin in which one sits to wash the whole body:
a white enamel bath with brass taps
A bath also means an act of washing one’s whole body at one time:
I have a bath every morning. (British English)
I take a bath every morning. (American English)
I’m just running/drawing a bath. (= pouring the water for a bath)
A bath is also a container for holding a liquid used for a special purpose:
an oil bath
an eyebath
The fabric is plunged into a bath of black dye.
Bath also means bathroom in advertisements for houses:
two bedrooms, kitchen and bath
to bath is to give a bath to (a person):
She’s bathing the baby.

Bath and bathe: Usage

In British English, bath and bathe have slightly different meanings. You bath to get clean:
He baths every morning.
to bath a baby
You bathe something to make it clean in a medical way:
to bathe a wound
to bathe one’s eyes
This difference doesn’t exist in American English, which uses bathe for both meanings. In British English bathe is also the word for swimming:
to bathe in the sea