Quite personally, I would go ahead and book it. You played fair by laying out both hotels for the other girl AND by repeatedly trying to contact her and text her. I think she would know that time is of the essence. I may be a b*tch, but go ahead and book it, plus there is always a refund/cancellation policy for hotels so maybe you want to find out what that is before you book to make sure it can be changed if the bm disagrees or throws a fit.
text her that for price and planning purposes, you guys need to pick a date, and you understand that she's busy, but if she's not able to get back to you by (blank time) then you and the bride will just have to go ahead and pick one.
if you guys were looking at three possible dates anyway, and now it's narrowed down to two, you know that those were possibilities for her, so either day would prob work for her (though it sounds like she may be the type to throw a fit and claim it isn't)
she's outnumbered here - and it's selfish of her to hold off someone else's bachelorette party b/c she wants what she wants.
the bride wants chelsea, the bride gets chelsea. period.
If the hotel has a simple cancellation policy, I would book both weekends you are considering and then cancel the one that doesn't work out.
Hermione's idea is good too. Text her and give her a deadline for responding. Tell her that if you don't hear back by X, you will assume that the date you and the bride have selected is ok for her.
I would just go ahead and book the weekend that is best for everyone else at the hotel in Chelsea, after all it is the bride to be's party and that was her choice. Whether the other bm is busy is not the point, surely she can find a spare moment to reply to a text message.
Just make the plans then notify her what they are. If she questions them, reply that you gave her ample opportunities to add her two cents and she didn't.