Use bath for the noun — the tub, or the act of washing in one, as in "she ran a hot bath". Use bathe for the verb — to wash yourself or someone else, to swim in open water, or to be covered in light, as in "they bathed in the river" or "the valley was bathed in evening light". A quick check: if you can put "a" or "the" in front of it, you probably want bath.
The core difference
Bath is the noun for the tub or the wash; bathe is the verb for the act of washing, swimming, or being immersed.
- bath — noun, the tub or the wash: She ran a hot bath after her long shift.
- bathe — verb, to wash, swim, or immerse: She bathed the baby gently in warm water.
- bathe — verb, to cover in light or liquid: The valley was bathed in golden evening light.
How to tell them apart
Both words trace back to the same Old English root, which is part of why they look and sound so close. Bath kept the noun job — the tub itself, or the act of sitting in one — while bathe took on the verb duties, covering everything from washing a child to swimming in a lake to being drenched in light.
The mix-up usually shows up in writing when someone reaches for "bath" as a verb, as in a stray "I will bath later". In British English that use does turn up informally, but bathe is the standard verb in careful writing, so it is the safer choice for anything formal.