Dumpster rental may vary depending on the size of the dumpster. The usual sizes may come in 10 yards for the smallest that costs around $250, the medium size which is 20 yards in length and usually costs $365, and the largest which comes in 30 yards amounting to $450 and up. The length of the rental dumpster can significantly add to the cost of your Bridgeport dumpster rental. Some rental companies may give away discounts that may last from 4 to 7 days. Then they charge $4 to $12 a day after the first week rental.