No, I refuse to make my kids take responsibility for someone else’s irresponsibility.
In my bathroom, you could not reach a cell phone from the tub unless it was on the tub surround. As an adult, I can not reach the vanity from my tub. I know my seven year old can’t.
In my house, if a cell phone or other object is left lying around, it is not against the rules to pick it up. With two kids a year apart in age, shared property is the default. Things that are “special” need to be identified as such. (The constant chorus of “MINE” is overwhelming without this rule - its bad enough with it). We don’t have enough strangers coming into the house to bother to have any guest stuff rules other than “you don’t dig through purses.”
In my house, my tech saavy kids would not have recognized many cell phones as cell phones. Dad carries a Pocket PC, Mom carries a Blackberry. My kids wouldn’t recognize the pink or blue clamshells that are the default cheap phones for teens as phones (now that they are almost eight and nine they probably would - six, with the case closed, I doubt it). They also have no clue that dropping electronics into water is bad.
In my house, six year olds did not get allowances, therefore making the child pay for the cell phone would be a meaningless punishment anyway. (My kids started getting allowances at about seven - we tried a few times before that, but money was meaningless to them until about the middle of first grade - and my kids both started first grade around seven).
So, would I pay for the phone? - if my kid grabbed the phone off a belt holster or grabbed it from inside a purse, yeah, I’d pay for the phone (it didn’t occur to me that the words “picked up” in the OP meant “took from purse or removed from belt”) - they wouldn’t have, they didn’t have money. But I didn’t get the impression that happened here. I got the impression that the phone was lying close enough to the bathtub to be picked up by the child while they were sitting inside the bathtub and was then accidentally dropped - and in my house that means it was on the bathtub ledge. Leave your phone on the bathtub ledge while there is a child in the bathtub, well, that was stupid. Have your phone sitting on the bathtub ledge while my kid is in the bathtub and I’m paying you to watch them, and I’m wondering what your phone happens to be doing out while my kids are awake and I’m paying you to babysit.
As I said in my first post, I’d probably pay half anyway. But I wouldn’t feel like my kids bore much responsibility if it played out the way I’m seeing it.