This study proposes the unit Gamma-Lindley distribution, a novel bounded statistical model that extends the flexibility of existing distributions for modeling data on the (0,1) interval. The proposed distribution is characterized, by closed-form expressions derived for its cumulative distribution, probability density, and hazard rate functions. Some statistical properties, including moments, order statistics, Bonferroni, Lorenz curves, entropy, etc. are examined. To estimate the unknown model parameters, several estimation methods are introduced and their performance is assessed through a Monte Carlo simulation experiment based on bias and mean square error criteria. A real data application focusing on firm management cost-effectiveness highlights the practical utility of the model, demonstrating its superior fit compared to current distributions, such as beta and Kumaraswamy. Furthermore, a novel regression model is developed based on the proposed distribution, with parameter estimation performed using the maximum likelihood method. The new regression model provides an alternative for analyzing bounded response variables. The findings contribute to the statistical literature by offering a flexible and comprehensive modeling framework for bounded data, with theoretical advancements and practical applicability.