i think both make sense!

They are the same. Have a bath (chiefly British English) Take a bath (American English) You can also say: I usually bath (UK) / bathe (US) right before I go to bed.

to take and to have, are both verbs. here you may be having a hard time with the fact that these are verbs being used in a special way, they are meaning of the verb is being put into the noun. She took a shower. vs. The children should have a bath before dinner. Will you have a drink? vs. She took the drinks before I could have one. I think context is important. Simply asking "take a bath" vs. "have a bath" doesn't make sense. Its like comparing apples and oranges. to me "have a bath" implies a command, but than it should be "take a bath." One does not simply hand out baths like candy or beer, "Dude, have a bath. Here take it." that use seems problematic. Or maybe your asking someone if "they have a bath at home." All of this is packed into the statement "have a bath" and therefore is too ambiguous to ferret out what you are saying or trying to say. Where as "take a bath" is fairly straightforward. It says exactly what it means- a command to "take a bath."