Critique
Hi! The idea is intriguing, although I'm not sure I really like it. Your writing is certainly good and you know how to build atmosphere. But I have to admit I find it hard to picture Snape in the position of the submissive. Don't get me wrong, I certainly *can* imagine him having a taste for punishment and being ordered to to something, for two reasons:
He might enjoy being 'forced' to do things, because in that case somebody else takes on the responsibility for his actions and the thing with punishment is, that after you've suffered through it, you have 'paid' for your misdeeds - real or imagined -, you are forgiven (something he seems to have a hard time to accept if freely given). So, yes he could be pictured as a convincing bottom, who would I.O. very likely have masochistic tendencies.
What's difficult for me to see is, that he would enjoy the submissive position. It would mean, putting somebody elses need before his own and being happy to serve without asking anything in return. The way you build it so far, he wants this to be about himself, experience something he has missed his life and experiment... Simply put, his reasons for doing this are centered on his ideas and wishes, he's doing it for himself. Maybe he doesn't know what he's asking for and this story is going to change in later chapters when he and Hermione realize the differences, but to be honest, I am not counting on it. But I will continue reading on and see how this develops.
Notice I didn't write about Hermione yet? I can see her as the person forcing people for their own good - to help them achieve what she *thinks* they want (S.P.E.W. anyone?). Serving by being strict, so to speak. But if this is going to be a BDSM love story as you claim, she doesn't seem to enjoy the dominant position in itself. It's a job, she is the one who has to cater to her customers needs, although she's most certainly hiding it from them. Key word here being *has to*. I get the feeling that's a necessity, not a part of the job she gets some personal satisfaction from. Her reward is the satisfaction of the customer, not her own. I miss the part of herself she invested unconditionally in her undertakings in canon, what ever might have happened to Hermione Granger to bring her to this point? In the books, she certainly invested a lot of personal convictions and feelings in everything she did, she seems to have lost an important part of her personality - of course it could be part of a history you plan to elaborate on, but so far it seems very OOC.
One last point, but one that is dear to me: I don't think she (or the professional dominatrix you portrait her as) should be chatting about 'I have this customer who likes...'. Even if it's just to put a newbie at ease and that customer might not even exist for real. She could have given examples without mentioning personal involvement. Snape came to her because he had heard of her discretion and professionalism after all. Something like that in the first interview should have sent him running...
I hope you aren't offended by my observations and me pointing them out. These are just some points that rub me the wrong way.