Hi Kirk,
Yes, you can run the wire along a barb wire fence instead of burying it but please note Pet Safe does have a disclaimer when it comes to wire/metal fences: "It does not matter if metal is galvanized steel, aluminum, wrought iron, etc. Metal of any kind has the potential to interfere although MOST will never notice any issue with reduced range, inconsistency.
Unfortunately metals can cause interference or a reduced signal. A large number of customers have used wired containment along fence lines for years with no issues.
It is important to note that this has always been the case with containment and that is why we suggest in the manual to lay out everything and test the system."