Knowing it is a small bear, and likely a sow, I'd have tried like heck to make sure there were no cubs. IF I was "sure", though, I'd have shot her. Would probably let her walk and risk losing her, to try and determine if she had cubs. However, with the behavior, probably not shooting even after 10 minutes. So far I'm 3/3 passing on sows with cubs, really want to go 4/4 rather than 3/4.
If I do kill a sow with cubs, I will feel bad, but at least know I genuinely tried to make sure she didn't have any. I do have an advantage in having worked quite a bit around nuisance bears, so have a better idea than the average unsuccessful hunter wanting their first bear. I have registed dozens of bears in WY, and received teeth from dozens of successful WA hunters, so I've had the opportunity to talk with several inadvertent cub orphaners. I have never talked to a successful hunter who admitted they deliberately orphaned cubs; of the guys who killed sows with cubs, I'd say 90% felt really bad, a few are like "oh, well, stuff happens" (some of the latter I suspect knew the bear had cubs, but I am not sure).