Great idea! Dress rental businesses are a great business model.
There are a few apps that actually allow this exact integration with dress rentals. Then you can use a subscription app to show those products only to specific customers.
You can also reach out to these app developers for support in setting up that integration or if you have any questions.
For a subscription app, check out some of the ones offered here and see what would fit your business case best. Some of them also offer loyalty features and much more.
Try that out and you can create and track rentable products behind a subscription.