I was sent home the same day & advised not to shower until the following night, which I did.
The cath cardiologist cautioned me against baths in general, not just after the cath -- especially WARM baths -- because of my general heart condition (mitral regurgitation plus systolic LV dysfunction).
I said, But I generally take very warm showers. She said that was different -- something about having the water hitting your body at different places being OK but not all your body at the same time as in a bath.
I didn't ask for more details because I don't normally take baths, just showers. The only reason I asked at all was because I was scheduled to go for a day of spa treatments with friends a couple of weeks after the cath. I had already figured out I probably shouldn't do the mud bath or the steam bath (both very hot), but I thought I could do the whirlpool if I kept the temperature down. She said no. So I ended up just having a massage, while my friends had the full panoply of treatments.