Not trying to talk you out of using the bio-oil -- but my guess is the only reason EP is using a bio oil is to (a) promote how 'green' they are and (b) jack the price up. Again, I'm guessing, but I suspect standard oil with the same properties might last longer.

One caution: it's possible that bio oil is easier to clean up, if it leaks into your pool. If your EP set up has the pump in a submerged location, where oil leaks would enter the pool, then the use of bio oil might be valid from an engineering or functional perspective.