Can deaf people not speak either?
First, good for you for not treating her like someone out of the ordinary. Second, some deaf (from birth or not) can speak, some quite well, some not well at all. Speaking can be learned even if you can’t hear. Those who lose their hearing later in life remember how to speak, but it tends to get sloppier over time, without the reinforcement of hearing it. Third, if you’re interested, you can take sign language courses. It’s not that difficult to learn (I know the basics) and, if you’re good with languages, it’s just another language. (ASL isn’t English done by signing – it uses English words, but it’s really a different language. There are, for example, puns that make no sense in English, but are funny in sign.) If you can’t find a place that gives ASL courses, if the deaf woman comes in again, ask her – she might know. (She can probably read lips – even hearing people can, to one extent or another. Women are usually better at it than men.
