In case it's still helpful after this long time: You can give anyone you like the capability to add slots (see https://docs.moodle.org/39/en/Scheduler_Module_capabilities). However, scheduler isn't really designed for the *same* person adding slots and also booking them (see CONTRIB-4218). Hence, I'm not sure whether what you intend is really feasible.
Scheduler (plugin)
Settings for students to Add slots and Book them?
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