Look for freshish cowpats and if there are any go somewhere else.
Indeed!
Last year saw me making a hasty, and half naked, exit from a field when, just after sundown I suddenly smelled cow, opened the tent and found that my previously empty field was now not.
I was now sharing it with about 20 very curious cows who were 50 yards and closing.
Thankfully I keep a tidy camp so was able to pick up and move bike and tent out and over the fence in about 3 armfulls ( never going back inside the tent, to then disappear from sight might be a really bad idea )
The next field wasn't as flat but at least it was properly empty.
Given my knowledge of cowpoohology is limited to the fact you can throw dry ones like frisbees, yes, the safest thing is, as you say, to go elsewhere.