Getting a horse rider’s attention

Has anyone seen any advice from horse riders on the best way to get their attention when trying to pass them from behind? I was out on a ride the other evening, and came up behind a horse on a downhill section of quite a narrow road. The rider seemed completely oblivious to my presence. The horse was trotting along, but seemed quite skittish, so I didn’t really fancy trying to get past without the rider knowing I was there. I was worried that shouting to get their attention would startle the horse, but didn’t really have any other ideas. In the end I rode slowy a safe distance back until she eventually turned off about a mile later, having not looked behind her once. I know there are periodcally complaints from horse riders about inconsiderate cyclists, and I don’t want to add to any us & them bad feeling, so it’s a genuine question to see if there was a better way of handling that situation, or if the only option is to hang back and hope they see me.