As Macpack said, I would have a very straightforward conversation in which your expectations and rules are clearly stated and if she still wants to ride the horse whenever she wants, regardless of you (his owner!), it's time for her to find another horse.
Have you seen her ride him recently? Is she heavy handed? My horse doesn't wear a flash either and if someone exercising her for me told me that they wanted to put a flash on her, I'd tell them to get tae ****, as they say here.
That said, I think it can be handled in a mature and diplomatic fashion:
"I really appreciate you helping me out with Bandit during the week and I know you enjoy riding him. As you know, due to my work I am only able to ride him myself on the weekends, and if you want to ride him during the weekend, it is very important that you contact me first to make sure that I have no plans to ride. I don't think it is fair on him to be ridden twice per day.
I am also making no changes to his tack, as his current set-up suits him and has worked well for a number of years.
I'm sorry to say that if you cannot follow these rules, then you will unfortunately have to stop riding him."
Or something along those line.
I'd do it via email or text, as I'm (a) really bad at confrontation and (b) I'd want this plainly written down so if I ever had to refer back to it, I could: "This is the email where I said that you couldn't change his tack and now you've put a flash on him" and then chuck her off your horse.
Edited as I crossposted with waresbear: I really don't think the burden should be on the horse's owner to text the girl exercising it for free whenever she plans on riding. It's her horse. She can ride whenever she wants! She should say, only once, that the girl should not ride on weekends and that should be that.
Last edited by thesilverspear; 12-22-2012 at 12:53 PM.