redcloud, I am glad you and your family enjoyed your bear encounter. All of my bear encounters in the Catskills and Adirondacks have been similar. Most times the bears scamper off immediately. Occasionally they give you a good curious look-over before leaving. And on a few occasions they just ignore you. Earlier this year I unintentionally stumbled within 12 feet of a small mother bear with two very small cubs, and they never even turned to look at me. I just stopped and allowed them to graze on, then I followed a bit from a greater distance until we parted ways. It was an amazing laid back experience.
When I go on midweek berry hikes in the Catskills I actually expect to see bears, and I am disappointed if I don't spot one. If anybody wants to see bears I would recommend finding a relatively unused trail with berry patches, and hike on a cool, overcast, midweek day. Bears are not generally too active during midday hours on warm/hot sunny days. If there are many hikers on a trail, chances are you will not see any bears as they generally avoid people.
An exception to that is in the Adirondacks where some bears have become aggressive at meal times and during the night at heavily used camping areas. Even then they only want your food, not you. Nor have I heard of any Adirondacks bears being aggressive toward hikers during the day while they are hiking.
So weapons are not necessary. As others have said making noise is your best bear defense. Chances are you will never need it.