There are many private bus companies that travel to eastern Europe weekly.
You can contact them yourself, in the picture below you can check a bit which companies drive to which area's in Poland.

Each region has own transport companies you can contact: Regio 1: Tony Transport, MAJBUS, Rafalski Bus, Buspl.pl, Mazurski bus
Regio 2: Rafalski Bus, Mazurski bus
Regio 3: Arnold Bus, StanTrans, Efect Bus, Vico Transport
Regio 4: StanTrans, Efect Bus, Vico Transport