I brought a homeowner's dryer gas line up to code. I billed the customer for my full time in installing and also charged the customer at the installation rate, for my figuring out the bill. She sqwaked. Doesn't everyone charge customers for billing time?
That might be considered "overhead" time. If you've advertised or communicated that the customer's cost will only be for the installation, then turned around and added something else, YES, she's got something to balk about.
You can either
(a) Bump up the installation cost to cover for the time you'll need - and stop making a surcharge. (b) "Eat" that extra time.
Then your customers have nothing to complain about.
Why she sqwaked? I mean how much time did you have to charge?
Usually you never charge for this. Why? Because before you start working you will figure out the bill. This time is basically free. For example, if a client approaches to me asking me to spend 2-3 hours figuring out his costs, I will not get paid for that time. It was estimation time and I see now way to charge him those hours.
Or other example, I brought car to the official dealer show and they spent 1 full day figuring out the error in my car system. They charged me only 1 hour for diagnosis. Imagine they charged me 8 hours just to tell me what's the issue and how much I have to pay to fix it.
IMHO you're on the thin ice. If you want to get that money, you should camouflage it under something else, although I don't think it's fair to your customer.