If the bike shop said they couldn't true it because the rim is bent, they shouldn't charge or at most a token charge only. They should be able to asses the wheel to see if that can be done at minimum when the truing job was started upon and the mechanic should have stopped the work on it and not charge for it.
This looks like they tried their best, spent time on it, while they should know better. Excusable for amateurs but not bike shop pros.
Also, even a mm out of true is too much for any decent bike. I like to have brake pads quite close to the rim when the brakes are not depressed. One mm would cause rubbing at each wheel turn.
I wouldn't like to do major truing job but was able in past to do smaller truing jobs myself, just using common sense and thinking or reading on it a bit. It helps to know about plucking spokes like guitar strings to check the tension and work both hub sides, loosening and tightening in tandem....
Last edited by vane171; 05-25-21 at 05:34 PM.