There comes a point you might want to add underwear for yourself! They like to grab things that float.
Have fun enjoy bath time.
DD has only ever taken a bath in the way you describe, OP. I never thought it was a safety issue, rather the opposite. Our first bath was an herbal bath after birth (mostly for me!) and we have amazing photos of her gazing into our eyes and smiling...just a couple hours after birth!
But since then, she has decided to hate baths with a passion. As in, I think it's bordering on abusive to force her to take them. Oh no, she loves splashing in cups and playing w/ the faucet in the sink. And she absolutely loved the ocean, and all pools. I wonder if it's the space or the noise...who knows. One time I was bathing myself and she saw me lie down (aka disappear) and she literally wet herself. I felt like the worse mom in the world.
Anyways, I can't imagine forcing her to bathe alone; it's hard enough together. As it is she doesn't bathe frequently... just a spongebath.*sigh*