No. Honey bee dysentery is not caused by a pathogen, so it is not “catchable.” Honey bee dysentery arises when the food a winter bee eats is high in solids, usually known as ash. These solids hold water in the gut and cause it to become distended. When the bees endure long periods of time when they cannot fly out of the hive to relieve themselves, they end up defecating inside the hive.
A common disease caused by the microsporidian Nosema apis, also causes dysentery-like symptoms. Nosema apis is a type of fungi that lives in the honey bee gut. The infected bees are unable to properly digest their food, which causes diarrhea and distended abdomens. Symptoms usually show up in late winter or early spring after long periods of confinement. As a result, the disease causes more problems in areas with long winters. A laboratory analysis is required for positive identification of a Nosema infection but, in any case, Nosema is not transmissible to humans.