Yes T1, I'm with Backpacker on this, the charge was fair. I'm sure it's adding insult to injury that you had to pay someone else to fly a plane you would have liked to have fly, but sometimes life's circumstances happen that way. (I remember having to hire a helicopter once for a two hour recovery mission into the bush, oh how much I wanted to go! But, I had another more important task then). This is a time in life when you can choose to be big about things. The airplane operator is not ripping you off, they're just in business. It'd be difficult for the operations manager to justify to the boss not charging you.
But, hint for next time... be the person... Be the person who is just "around" the airfield in your spare time, it's amazing what comes up! I was that person, the airport rat, always around doing something, and that something was always interruptible to go to pick up or deliver a plane. This time, someone was the person to your problem, next time be the person for someone else's problem!