Brighton and Hove Buses said incidents had been reported at Brighton Marina, Mile Oak, Western Rd, North St and from Rock Gardens to Whitehawk.
The company's police liaison officer PC Jay Jackson said often bus drivers didn’t know this was happening because they couldn’t see.
PC Jackson said: “If a driver is aware that this is happening they will stop the bus immediately and call our response team and the police. The trouble is, by the time we get there the perpetrators have usually gone.
"Young people are risking life and limb by doing this and I’m asking them to think about how serious this could be: for themselves and for their families."
PC Jackson said that where youths were identified wearing particular school uniforms, he would visit these schools and to speak to children and teachers.
Martin Harris, Brighton and Hove Buses’ managing director, said: “There appears to have been a spate of this behaviour, recently. It's an incredibly dangerous thing to do and I’m imploring people not to try it under any circumstances. Don’t put your life at risk for the sake of a stupid dare and wreck Christmas for yourself, or your family.
"If you do see this happening, please report it immediately to the police on 999. The police will also ensure that our police liaison officer and our control room know about any incident, if they aren't already aware of it."