How should one properly discard a Lulav, Esrog, and the Hadassim bundle? Can they be thrown away in the regular trash, or do they possess Kedusha?

The best way to discard the Lulav and Esrog is to burn them with the Chametz before Pesach (Mishna Berura). If this is not possible, these items are Tashmishei Mitzva, Holy articles used for a Mitzva, and one should place them out in a field or somewhere where they will not come to desecration. They do not need to be put in Geniza. Some suggest that one can dispose of the four species by placing them in a bag and then in the trash. Since they are wrapped separately, it is considered as if they are not with the other trash.