Answer: Rambam (Bikurim 5:13) writes that the challa which one is supposed to separate and give to the kohen is akin to teruma. Just as teruma which becomes tamei must not be eaten, so too challa nowadays may not be eaten as we are all presumed to be tamei. Likewise, any dough that came into contact with water or any of the other seven liquids would be tamei (See Mishna, Machshirin 6:4). According to Rambam (Yom Tov 3:8), there is a mitzva mideoraisa to burn this tamei challa (See Tosafos, Shabbos 24b). In chutz la’aretz where this mitzva is only miderabanan, the requirement to burn it would also be miderabanan.
Thus, the Rema (YD 332:5) writes that nowadays we burn this dough. As only kohanim may benefit from challa, it must not be baked together with other bread, though. While the Shach (YD 108:1 quoting from the Issur Veheter) writes that one may bake this challa in the oven together with one’s bread, the Aruch Hashulchan (YD 108:9) writes that one must wrap the challa first to ensure that no steam escapes.
Burning the challa, however, has its disadvantages. Especially as one is supposed to ensure that it doesn’t come into contact with other foods, it can take a while to properly burn through. R’ Yitzchak Yaakov Weiss (Minchas Yitzchak 4:13) adds that if one leaves the challa around until it is convenient to properly burn, it may get eaten or placed with food. In this case it would certainly be preferable to wrap it before placing it in the bin.
In conclusion, if it is easy for one to burn it properly away from their food one should do so. Otherwise, one should wrap it and place it in their bin.