yep you can usually store your hired equipment at the hire shops. had no problems with doing that last year. most of the hire places are near the slopes...
As far as the Rila 1 ski depot is concerned you go in wearing your normal footwear in the morning and swap for your skis, boots etc and go off skiiing.
Come back at the end of the day, hand in hire gear and collect your shoes, get changed and go out to party. No worries about storing gear