The verb bath is used in British English mean – ‘wash ( yourself or someone) in a bathtub’.
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’..
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.
But in American English, bathe is used to mean ‘take a bath’, same as the verb bath in British English.
I like to sunbathe when I am on the beach.