In a metro this size, a few things move a Houston dumpster price more than others.
Container size comes first. A larger container costs more, but choosing well up front saves you from overage charges or a second haul.
Weight is next. Wet drywall, shingles, tile, and concrete add up quickly, and a container can hit its tonnage allowance while it still looks half full.
Distance matters here more than in most cities. Harris County is wide, so the trip from your address to the landfill that takes construction debris is part of the price. The landfill that commonly takes that debris is privately run, and it quotes disposal by account instead of posting a public rate.
Time can matter too. The City of Houston adds a separate storage permit for a container that stays on a property longer than 60 days, so a short rental avoids that cost entirely. Your account manager will walk you through the disposal and timing side of your quote before you book.