I'd use air!
You didn't state the diameter, depth or static water level.
Speedbump is right, the pump you are referring to is called a bailer it is used on cable tool drills. It's basically a 5' to 10' of light weight metal pipe or PVC just smaller than the well casing with a dart valve or leather flapper valve on the bottom. (A flapper valve is not unlike the flapper valve in a pitcher pump wit a steel weight bolted in the middle. It's run in the well with a rope or cable, then when on the well bottom it is raised a foot or so and dropped several times then pulled out and dump the silt out of the bailer. This is repeated until a satisfactory depth has been reached. It's an old outdated method but it works. Existing cable tool drillers use it today.
I prefer cleaning wells with air by running a 3/4" rubber air hose or good grade rubber garden hose with a 4 foot galvanized pipe on the well end and run it in the well. Hook the other end of the hose to a reasonably large air compressor (35 to 150 cfm), turn on the air slowly at first, then when the water starts coming out the casing, increase the air and lower the hose deeper in the well as it blows out the silt and sand in the well.
Look out it's going to blow water, air, sand and silt everywhere. You can divert it through a Tee on the casing.
Once it is clear of sand and silt pull the line up and continue to blow until the water is reasonably clear of sand and silt.
This same method is also great for testing the well for flow, pumping level and static water level. These can be found by using an air gauge on the hose to monitor the air pressure immediately after blowing the well and again in 30 minutes after the well has set idle. Multiply the air pressure on the gauge times 2.31. the result will give you the amount of water remaining above the bottom end of the air line when you stop blowing. After waiting 30 minutes (If there is no leaks in the air line) read the air gauge again, multiply the resulting pressure times 2.31 and the result will be the amount of water above the end of the air line. Subtract this result from the total length of the air line and it will give you the static water level (when the well is not being pumped).
Good Luck with either method.