The WestlawNext site has some informative user guides and brochures, including a chart that compares features of the current Westlaw and WestlawNext. I was interested to read their comments about the use of The Bluebook citation format in WestlawNext. In one of the brochures, they talk about having

Copy and paste with citation, including Bluebook. You can paste text
into your work product with the official citations — including The Bluebook, ALWD, California, New York and other leading formats.

It seems that if you “copy with reference” it will include a Bluebook citation by default, and you can choose other formats by clicking on the preferences option at the bottom of the screen. I am looking forward to seeing a live preview of the new interface!