Are there any STP liquids not containing large amounts of hydrogen and oxygen that are safe for human contact?
Perfluorocarbons would be a possibility, $\ce{(-CF2-)_{n}}$, they contain only carbon and fluorine and are relatively low cost and widely available in large quantities.  They are inert (e.g. non-reactive) and depending upon chain length and structure, you could pick one that can be warmed up nicely to a bath temperature.  They are also used industrially in degreasing operations, so they might have some cleaning ability as well.  

Some perflurocarbons are actually being investigated as human blood substitutes - they can transport and release oxygen to tissues.  Perfluorodecalin is a prime example. As shown below, it is basically a naphthalene ring in which all of the hydrogens and double bonds have been replaced with fluorine.



Ingesting small amounts would not be a problem. In fact, these same materials have been used in liquid breathing experiments.  

There are a number of other scientific aspects of these perfluorocarbons that could play into science fiction.  For example, the small size of the molecules (compared to say, haemoglobin) allows it to travel to smaller places that haemoglobin cannot access due to its larger size. Perhaps the perfluorcarbon could also carry small drugs to relax, rejuvenate, repair body parts, or enhance sensory experiences during the bath. Since these perfluorocarbons act as oxygen transport agents they could also be worked into the story as a bath medium that also scavenges "loose" oxygen.