You can get some of the 5 gallon food grade jugs (or smaller) and fill them before you leave, or fill them at the campground. Do check that your campground has potable water available. Many people travel with them in the tub/shower. If the water source is a ways from the site, you can use a 2 wheel dolly to transport them.
You can also invest in some type of larger food grade container that lives in your truck bed, if you will have a pressurized source to fill from. If there is enough height difference you can fill the tank by gravity, starting a siphon by mouth, or you can get a 12 V pump to use with it.