Decomposition of a word into a set of appropriate pseudo-characters is a challenging task in case of a cursive script like Bangla. Segmentation-free approach bypasses the decomposition problem entirely and treats the handwritten word as an individual entity. From the literature, we found that the accuracy of handwritten Bangla cursive word recognition using segmentation-free approach is relatively low (accuracy hovers between 80% and 90%). In the current work, we aim to provide a threefold study on this particular domain. Firstly, we extract different statistical feature sets from word images and use five different off-the-shelf classifiers to delineate their performance. Then, we employ five different CNN-TL architectures, namely AlexNet, VGG-16, VGG-19, ResNet50, and GoogleNet, to understand how they perform on holistic Bangla words. Finally, we use a seven-layer FCN architecture and provide a comparison of results with all the aforementioned experimentations. We achieved an accuracy of 98.86% with ResNet50, which is nearly 19% improvement when compared with other recent state-of-the-art methodologies.