A real-time Bangla Sign Language interpreter can enable more than 200 k hearing and speech-impaired people to the mainstream workforce in Bangladesh. Bangla Sign Language (BdSL) recognition and detection is a challenging topic in computer vision and deep learning research because sign language recognition accuracy may vary on the skin tone, hand orientation, and background. This research has used deep machine learning models for accurate and reliable BdSL Alphabets and Numerals using two well-suited and robust datasets. The dataset prepared in this study comprises of the largest image database for BdSL Alphabets and Numerals in order to reduce inter-class similarity while dealing with diverse image data, which comprises various backgrounds and skin tones. The papers compared classification with and without background images to determine the best working model for BdSL Alphabets and Numerals interpretation. The CNN model trained with the images that had a background was found to be more effective than without background. The hand detection portion in the segmentation approach must be more accurate in the hand detection process to boost the overall accuracy in the sign recognition. It was found that ResNet18 performed best with 99.99% accuracy, precision, F1 score, sensitivity, and 100% specificity, which outperforms the works in the literature for BdSL Alphabets and Numerals recognition. This dataset is made publicly available for researchers to support and encourage further research on Bangla Sign Language Interpretation so that the hearing and speech-impaired individuals can benefit from this research.