Also! it is still worth it to rub your hands together in the water if the bathroom has no soap -- one study showed bacteria reduced by almost half from water alone.
"Bacteria of potential faecal origin were found after no handwashing in 44% of samples. Handwashing with water alone reduced the presence of bacteria to 23%. Handwashing with plain soap and water reduced the presence of bacteria to 8%."
Show Me the Science – When & How to Use Hand Sanitizer in Community Settings