I have asked this question to a number of rebonnim and have not heard an answer.
Why is there no custom to have separate milchig and fleishig garbage bins in our kitchens? The issur of bishul boser v’chalav applies even if we don’t eat it. I often find myself throwing a hot, milky teabag (for instance) into the bin which still has the remains of last night’s meaty supper. We are all machmir to have separate meaty and milky work-tops in our kitchens, where usually it is just the kelim which touch the worktop – surely separate bins should be even more necessary, since there the foods themselves come into contact.
In answering this question, it is important to note that although various authorities quote the concept of a davar gush (solid body) as being able to “cook” (see Magen Avraham 318, Nishmas Adam 20:3), it remains a chumra that is widely disputed (see Rema, Darchei Moshe 105:4, Pleiti (ibid.), Chasam Sofer YD 95, Shut Pnei Yehoshua 2:23, and others). This opening point gives the following considerations significant weight.
1. Davar She’eino Miskaven: See Iggros Moshe YD 39, Yad Yehudah 92, among others, who write that (like other prohibitions) the prohibition of cooking meat and milk does not apply where it is a davar she’eino miskaven. In our case it is hard to call the single garbage bin a “pesik reishei” for mixing meat and milk — by the time the teabag gets thrown in it might be cold, it might not come into contact with the meat, and so on.
2. According to many sources, the prohibition of cooking meat and milk together is due to the concern that one might come to eat the mixture (see Kesef Mishnah Tumas Mes 1:4). Accordingly, where there is no chance of this happening, some authorities are lenient (Dovev Meisharim, Har Tzvi).
3. Even if a davar gush cooks, it might not be called “derech bishul” to prohibit the cooking of meat and milk together (see Pri Megadim, Intro., s.v. Od Adaber).
4. Because both foods are (usually) already cooked, some authorities maintain there is no longer a prohibition of cooking meat and milk (see Chasam Sofer YD 82; Pri Toar 87:3; Aruch Hashulchan 87:13; Machazik Berachah 87:12).
The combination of the factors above would seem sufficient to permit the use of a single garbage bin for meaty and milky.