Vampires are not supposed to be able to cross MOVING water, so rivers, the sea etc. A bathtub should pose no problem. A lot of vampire weaknesses come from the fact that they are impure undead, both garlic and silver were said to have purifying properties back then. The idea that vampires don't show up in mirrors also stems from that, old mirrors were made using silver behind the glass, so their reflections would be "purified" and not show up.