Guernsey Police said it happened between 08:40 and 09:00 on 30 September.
The incident occurred on the number 42 bus – which carries passengers between town and Vazon, stopping at the top of the Grange, the Rohais, L’aumone, Saumarez Park, the Houguette, and other stops in both directions.
A police spokesman said “an adult male is alleged to have acted inappropriately towards two juvenile females” while this bus was carrying passengers on Monday morning.
“If you have any information regarding this incident, you are asked to contact PC 110 Browning on 222 222 or to contact Crimestoppers anonymously on 0800 555 111,” urged the spokesman.