Does Asuna speak English? In episode 5 of the English sub of Sword Art Online: Alicization, Asuna infiltrates the Ocean Turtle facility disguised as Mayumi Reynolds. 

When she arrives at the facility, she says "nice to meet you" to the guard who greets her in English. Further in, when another guard asks her to remove her sunglasses and confirm her identity, she replies "sure" in English.

Does Asuna have any significant English speaking ability? Or did she simply learn a few words in order to solidify her disguise?
Yuuki Asuna went to an all girls private school before the events of SAO. So I'm pretty sure she would have learned it at her school during that time. Most Japanese schools teach English as a curriculum. But sadly a lot of Japanese people still don't have "fluent English conversation abilities".

Considering how serious she was about clearing the game, I would guess that she probably also took her school work very seriously. And hence most definitely picked up the lot of the English phrases which she then used in SAO.