I have 5 children.....I am never more than a "step" away (literally) from going in and helping the 7 and 6 year old girls....I am usually in the bathroom "doing" something (usually cleaning up dried toothpaste from the sink, but that's a whole other post!)...or right outside the bathroom door...so the second I hear "Mommy!" or I hear a bang that isn't familiar, I'm right there...
My 5 year old....she takes baths and I leave the door open to dart in and out (again, still only right outside the door folding linens or something...
I don't think, with water, you can be too cautious....it was just a week ago that my 5 year old was laying down in the water (I never have it too high so her head is covered...she was laying there, face sticking out...) and I was walking in and out...kept glancing down at her..and within just a minute or two, she'd fallen asleep in the tub...
If I hadn't been right there I wouldn't have noticed...and maybe she could have turned over and drowned? (Okay, the likelihood of her not waking up would be slim, but certainly would have caused problems had she rolled over and breathed in bath water!)
Sorry to go on about this...but as a former child protection worker...I did see true "accidents" with infants and toddlers in the bathwater...also know of a situation where a child was in the shower (3 year old) and slipped and broke his arm...(an accident, but still.....)
I would never do it.....is it worth the risk? I take my phone in with me....use that time...while I'm sitting NEXT to the tub/shower.....to chat with a girlfriend, to pay some bills, to balance my checkbook, to make my grocery list....you can multi-task while your child is in the tub...
Good Luck and sorry for babbling...