In BrE, we "have" a bath, rather than "take" but of course we understand what "take a bath" means. All 6 of your sentences are grammatically correct. I find the use of the verb "to bathe" rather formal for this context. In addition, "to bathe" can mean "to swim in the sea".
My BrE versions of your 3 sentences would be:
1. Have you finished having a bath? (or "Have you finished your bath?")
2. Have you had a bath?
3. Did you have a bath yesterday?
Student or Learner