If you do not desire to purchase a pistol, you could apply for an Eligibility Certificate to Purchase Long Guns which would also cover ammunition. You have the right to protect yourself on your property, with that said taking potshots at bears just because they are on your property will land you in court. In your house, glassed in porch different story. I would suggest not keeping any food items/bird seed/trash etc.on your porch. If the bear can smell it, it will come get it. Concerning your property size, if you are hunting with a shotgun on your property make sure you are not within 500 feet of any other occupied dwelling, buildings, etc. Remember there is no bear season in CT. Archery would be allowed as there is no acreage limit. Make sure a signed consent form is being carried by anyone hunting on your property. Be mindful of surrounding neighbors as we have been dealing with a lot of archery hunters shooting deer on small parcels of land that run onto neighboring properties they don't have permission to be on to retrieve. This is causing a lot of controversy and portrays a poor reflection/image of hunters.