Were it my coach, I would pay her day fee, which is $1200, plus any travel and hotel stays.
Needless to say I usually just send her a video and then show up with the horse for her to see haha!!
Were it a client paying you a commission, then your commission should be enough to negate a day fee, but you still would charge travel. In that case it would be you having found the horse, made the appointment, etc.. Because the rider found the horse, you have really no obligation to see it outside of watching a video, or if she gets a trial, looking at the horse on trial.
They say money doesn't buy happiness -- well happiness doesn't buy horses!