>>37838
>>37805
Many apartment complexes have a large shared dumpster. It sounds like yours is a little different because of your trash bag situation, but I would check the full complex just to be sure there isn't one. Even if your apartment does not have one, oftentimes one apartment complex will be near another and you can dump there. If not, there are often large dumpsters behind restaurants, especially fast food. These usually say "no public dumping" but I have never had a problem.
I also suggest like the other guy that you do not need to use all 36 in 2 weeks. You're already putting things into moving boxes, right? So box up 30 or so of them in a normal moving box, put a layer of clothes on top, and label the box something boring like "Old clothes", "Storage", or "Yearbooks". When I moved, I threw my spare diapers in my gym bag, a duffel with a tiny lock on the zipper. With all the other things to move, nobody spared it a second glance even though I had seven people helping me move boxes. Gym bags typically smell bad anyway and are filled with random shit like clothes and water bottles so it's not very suspicious.