Check your laws in your area before shooting any living creature. There might be laws against the firing of weapons in your area, so if you shoot the rooster you are at risk of being fined or imprisoned (or your Dad). Also consider the risk of hitting a living person when shooting at a moving target. Nothing worse than to be shooting at a fractious animal only to have the bullet ricochet and kill Granny reading the bible in the next house.
If the rooster is attacking you, document the injury with photos, and check the laws about dangerous animals. Also document the rooster coming on your property and hassling your fenced birds. Remember your unrestrained birds might be going on your neighbor's property and irritating him or her. This could be the crux of the problem. Everybody has chickens going all over the place and scratching up the garden and so forth. Your chickens might be irritating the neighbors as much as that rooster is irritating you.
Talk to your neighbor again and make sure they understand the problem. Let them know what your intentions are if the rooster returns. Personally, I'd catch the dang thing and let the owners claim him. If they don't then dispatch of the rooster as you see fit. Remember, the rooster is simply being a rooster. He's doing what comes naturally, and his owners are at fault for not keeping him where he belongs.