Poland is Europe’s leader in international freight transport. The majority of companies in the Polish logistics sector are small-sized enterprises with limited human and material resources, which reduces their ability to implement corporate social responsibility practices. In this paper, we explore the logistics solutions (tools and practices) implemented by companies in the logistics sector to manage their business operations through the prism of the triple bottom line (TBL). We assume that a company might achieve sustainable performance even if it focuses mainly on the implementation of logistics solutions for economic performance, as some of those tools and practices also have an impact on the environmental and social performance without being dedicated to them per se. We define sustainable logistics management maturity (SLMM), as the extent to which a company implements modern logistics solutions (tools and management practices) to improve performance with regard to the economic, environmental, and social dimensions of sustainability. Results from focus group research are presented, where experts have assessed the impact of tools and management practices in logistics management on the economic, environmental, and social dimensions of sustainability. Then, we define the overall sustainable logistics management maturity indicator (OSLMI) to allow comparison and benchmarking between companies in the logistics sector. The maturity theory is applied, as it is a suitable tool for the positioning and benchmarking of companies. Through the conceptual model, we link the capabilities of a company (expressed by the application of the logistics solutions) with factors related to the company’s characteristics (size, business profile, source of capital), and the ability of a company to achieve a certain maturity level. The maturity concept is used here to measure the effectiveness of the performance of companies. We use a database of 190 Polish companies from the logistics industry to verify three research hypotheses. Bayesian statistics is applied to verify the existence of a relation between the level of SLMM and a company’s characteristics (size, scope of economic activities, and structure of capital). Statistical analysis proves that the size of a company and the type of economic activities it engages in affect its ability to achieve a higher degree of maturity.