Maybe, but they have to make a new plastic bag if they don't recycle your old one. Energy is required to make that new bag, which means CO2 is created that way too.

The best thing you can do is to not need so much energy in the first place. If you must travel use high efficiency transport. (shipping counts as travel). Make sure your housing is well insulated.

The next best thing store carbon: start forest and grass fires. A regular forest/grass fire will burn cold enough that a lot of carbon is converted to charcoal - permanently sequestrated carbon. Note that regular is key here. If you don't light a new fire every year fuel builds up until you get a hot fire.