Author profiling, the analysis of texts to uncover attributes such as gender and age of the author, has become essential with the widespread use of social media platforms. This paper focuses on author profiling in the Bangla language, aiming to extract valuable insights about anonymous authors based on their writing style on social media. The primary objective is to introduce and benchmark the performance of machine learning approaches on a newly created Bangla Author Profiling dataset, BN-AuthProf. The dataset comprises 30,131 social media posts from 300 authors, labeled by their age and gender. Authors' identities and sensitive information were anonymized to ensure privacy. Various classical machine learning and deep learning techniques were employed to evaluate the dataset. For gender classification, the best accuracy achieved was 80% using Support Vector Machine (SVM), while a Multinomial Naive Bayes (MNB) classifier achieved the best F1 score of 0.756. For age classification, MNB attained a maximum accuracy score of 91% with an F1 score of 0.905. This research highlights the effectiveness of machine learning in gender and age classification for Bangla author profiling, with practical implications spanning marketing, security, forensic linguistics, education, and criminal investigations, considering privacy and biases.