HPV baby transmit
There have been cases where hpv
has been shown to be transmitted from a parent to a child: during birth (with babies occasionally infected on the vocal cords), babies and moms sleeping together, and, yes, probably in bathing together as well.
The prevalence of hpv being as high as it is and the scarcity of cases of such transmissions being so low, you should consider the risk minimal. No worries!