Unless you have a drain, running water is not really very practical.
What would be the use for the sink?
A 1-liter soda bottle with tap water from home can do a very good job of hand washing, especially if you have mechanic's soap in a pump container. A 5-gallon bucket will catch the drippings.
Old guys who camp in the woods know that a half-gallon juice bottle with a screw cap makes a dandy urinal.
I would just bring a few liter bottles of tap water, a container of mechanic's hand cleaner, a juice bottle and an empty bucket over. Oh, add in a roll of paper towels. Total cost is under $5, and you have 99% of the functionality of a sink, with no plumbing and no digging.