I'm old school on this. I haven't researched anything more exotic since until the last decade I only used yearly appointment books. Most of the guys my age, mid-60s that I knew made all their own calls and scheduled their own appointments even when working at clubs.
If you have multiple venues and spend days driving from place to place, it always seemed best to control your own scheduling. I will say that I had a cell phone as early as 1987 installed in my vehicles for this purpose. Smartphones have made it much easier with texting and voice messaging.
My first big jump to technology was buying a $250 answering machine that I had to special order in 1981 just so I wouldn't miss calls for lessons at home or in the pro shop. They didn't have voicemail back then.
I bet there probably is a great application or subscription service that allows students to schedule without your help. It depends on how much you want to handle your own scheduling.
Good luck.