Great that you are enjoying riding with your mother, that is time well spent. I'll caution you about just buying a bike and giving it to her, that is a risky proposition unless you can use her previous fitting to buy one. Maybe a letter or card saying you will take the time to take her to the LBS and find the bike that suits her fit and her needs, all as your gift. You seem to understand bikes pretty well and to be experienced as a rider so I think you can understand what I am trying to say, poorly at that, sorry for my clumsiness. I'd hate for her to feel a gift bike had to be kept if it didn't fit her or feel right for her riding needs. My wife is your mother's age, save a year or two, and I let her chose any bike she gets, and there have been bikes as gifts, just not a "bike with a bow on it" always a trip or three to the LBS for her new ride when that happens.
Please keep us updated on her N+1 and maybe get her to join us here after the surprise, whatever you chose to do.
Bill