I recently began a new save file in Pokemon X, and I finally finished the Power Plant part of the game. I have reached Lumiose City, and the whole city is available to me now, including Estival Avenue and Alexa's guides. I read that if you ask her to show you around, it's a really good way of raising your style. How many times would I have to have her guide me around for me to be able to get into Boutique Couture?
Well, according to Bulbapedia, talking to Alexa raises your style by 5 points, you need 25 style points to be able to enter Boutique Couture.
So, you would have to talk to Alexa a total of 5 times to be allowed to go in Boutique Couture.
Hope this helps!
You can only get style points from talking to Alexa the first time.