If the tub is cleaned properly, the risk of an infectious pathogen would probably be fairly low. Most hotel tubs are not used for long periods of time (e.g. like a hot tub), and if allowed to dry in between uses completely, a viable growth medium for most pathogenic bacteria and fungi would be denied. Viruses are a bit more complicated, but most of them are biologically very wimpy and subject to destruction by common household cleaners.

If you travel by car and can carry a disinfectant solution with you (preferably a chlorine-based bleach), you can spray down the tub and let it sit for a few minutes then rinse it out just for extra measure. Chlorine-based bleach solutions are remarkably effective against most types of pathogenic microbes. Alcohol is the same, but I doubt anyone would want to carry a gallon of isopropyl alcohol with them! I won't suggest anything about carrying ethyl alcohol, however....