Slightly off topic: Booking time slots outside (or embedded) in Moodle.

One of these may work for you: calendly or acuity.  I have tried both, but ended up with acuity (who PAY the evil Google to get shown at the top when you search for calendly!!)

It may not give you what you say you want as described in this post; but personally, the fact that you are volunteers means your staff should do as little work as possible; get your students to book!!  (Off soapbox now)

Scheduling via this app has literally changed my life in a certain segment of my distance students.  Texts and email reminders to both parties.  I'll flick you my secret link if you PM me if you want to have a look at it in action.  

-Derek
Who has no business investment at all with either of these entities.

Hi Simon

Scheduler is really built for *teachers* offering times and students choosing from them, so I'm afraid that feature wouldn't be easy to add.

Best wishes

Henning