Is this referring to the bathtub? Or is it referring to the actual bath (like the water in the tub)? This sentence confuses me a little.
Yes, it refers to the bathtub.
In colloquial speech, it could also refer to the bathroom, because in colloquial speech we may use ва́нна instead of ва́нная.
Is ванна colloquially correct or colloquially slang, when referring to the restroom?