In this paper, we improve a recently introduced accelerated k-means++ algorithm by proposing a dynamic method for calculating bounds during its execution. This approach produces high-quality bounds without requiring a full iteration over the dataset, using the Triangle Inequality and the norm of the points for efficient computation. We propose three evaluation metrics to assess the quality of the calculated bounds and analyze their behavior across a diverse dataset. Results show that this dynamic method outperforms the traditional approach of initializing bounds at the end of the process, before the execution of the \(k\) -means algorithm.