The bigger hose will fill the bucket faster, because it has a larger diameter, and therefore more water can flow out of it. Hence the bigger hose has a bigger bandwidth. The speed of the water coming out of the hose is a function of the water pressure and gravity, not how big the hose is. We measure the speed of water in feet per second or meters per second, but we measure bandwidth in gallons per second or cubic feet per minute. So we measure Internet traffic, not in miles per second, but in bits per second.
Bits are like drops, and kilobits are like gallons.
When we download an image on the Internet we are not interested in how fast one bit of information is downloaded, but we are interested in how long it takes to download all the bits that make up the picture. If the size of the image is 33.6 Kb and the modem connect speed is 33.6 Kbps, then, in theory, the image will download in one second. In reality, it might take longer to download. The rate of data transfer is constrained by the narrowest pipe, or by the most congested pipe. The most congested pipe could be your ISP or the web server that you are downloading the image from.