The verb bath is used in British English mean – ‘wash ( yourself or someone) in a bathtub’.
Example
Dogs should bath regularly. (GB English)
On the other hand it is different in American English. Americans Instead of the verb bath are using the expressions ‘have a bath’ or ‘take a bath’..
Example
As I was feeling hot, I took a bath. (USA English)
In British English, bathe means ‘the act of swimming‘. This is very formal expression in British English.
If you want to use it in as informal expression ‘have a swim‘ or even ‘go for a swim‘ is what you need.
Example
She said she had a good bathe in the lake.
But in American English, bathe is used to mean ‘take a bath’, same as the verb bath in British English.
Example
I always bathe after game.
I like to sunbathe when I am on the beach.
I like to sunbathe when I am on the beach.
