I think your first sentence says it all. In a boarding barn, you’re generally free to come on your own schedule. In a true training barn, there is already a set schedule for staff/trainers/clients and you need to adhere to it. If every rider just wanted to come out and hack around at their convenience, it creates a huge inconvenience for the barn staff, trainer, other clients, etc. You decided at 4 PM on a random day that you want to take Fluffy for a ride but that’s the time someone needs to drag the ring or the farrier is there working or the grooms need to be picking stalls or trainer has already ridden the horse that morning, etc…
I’m sure the BM/Trainer (I think they are one and the same from your post) would be happy to accommodate but schedule the times in advance so s/he knows you will be there.