Seriously, do NOT. For more information, including disgusting examples and photos – see this article.
The fats in the grease and oil from your kitchen mix with the other chemicals in the sewers and form nasty conglomerations of chemicals that can build up and block the pipes that take our dirty water to the wastewater treatment plant.
Put your grease in the trash, not the sink.
Cook sparingly with oil – it’s easier/better to add more than to have too much. But you don’t get a choice with bacon. Storing in plastic containers are not a good idea, as they might melt if you don’t let the oil/grease cool. I use the leftover metal containers from canned goods. If you did enough volume, it’d be worth the time to make biofuel. One day, municipal services will likely provide such a means but currently they’re telling people to put the left over fat/oil in the landfill.