The collection of the organic fraction in Italy recorded significant growth in the decade 2010–2019 (+74%) due to both the increase in the spread of separate waste collection as well as the increase in the biological treatment plants of municipal waste. However, within the organic fraction there remains a share of non-compostable material (NCM) (plastic, glass, aluminum, etc.), equal to ~5% of the total, which affects the efficiency of composting practices as well as decreasing both the yield and the quality of the final compost, causing a portion of organic material to be subtracted from composting and ending up in landfills. Therefore, the purpose of this work is to evaluate how the sustainability of the organic fraction collection and the amount of compost obtained in the composting plants could improve, following the use of biodegradable and compostable bioplastic bags (shoppers), in replacement for conventional plastic ones. The Life Cycle Assessment (LCA) and Carbon Footprint (CF) methodology was used for the assessment, comparing two different scenarios based on data relating to the collection of the organic fraction in Italy in 2019. Scenario 1 relates to the composting of organic material that also contains plastics, bioplastics, and non-compostable materials, while in scenario 2 the share of plastic material in the first scenario has been entirely replaced by bioplastics. The results show that scenario 2 assumes the lowest values for 15 impact categories out of the 18 analyzed, and, among these, in three categories it assumes negative values: ozone formation-terrestrial ecosystems (−1.64 × 10−2 kg NOX eq), ozone formation-human health (−8.50 × 10−3 kg NOX eq), and fossil resource scarcity (−4.91 × 102 kg oil eq). Furthermore, scenario 2 has a negative carbon footprint (−3.80 kg CO2 eq) compared to scenario 1 (79.71 kg CO2 eq), and in general it is the most sustainable scenario as a direct consequence of the greater amount of compost obtained (307.4 kg vs. 269.2 kg).