No cover!
There is never* a cover at Le Bain, but all entry is at the door's discretion. If you are willing to partake of bottle service it can assist with entry, but this must be requested a few days in advance, or with the door the day of your arrival. *Except for their New Year's Eve party, which is a ticketed event.
Not as of a few years ago
I don't think so but I never got any cover there
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