The two people killed have been named as Susanna Gazorian, 22, and Yelena Tarasova, 17, from Pyatigorsk, a source in the Russian emergency situations ministry in Stavropol told the Interfax news agency.
A police official was quoted by Interfax as saying that the bomb was homemade.
The bus was parked at a station in the town of Nevinnomyssk when the explosion caused the bus to catch fire.
The local prosecutor's office in Stavropol region was treating the blast as a terrorist attack, RIA Novosti news agency said, quoting an unnamed official.
Other sources said the blast could have been caused by an exploding gas canister.
The latest blast came after a nail bomb exploded on a bus in the near by North Ossetia province on November 22, killing five people.
Russia's north Caucasus is a volatile region wracked by violence centred on Chechnya, which has fought two separatist wars since 1994.