We propose a new method for modeling and quantifying bounded Gaussian jitter (BGJ), as well as bounded Gaussian noise (BGN). The validity and accuracy of the method are illustrated and verified both in theory and experiments. We then demonstrate the applications of this new method for jitter and noise estimation and testing, especially for total jitter (TJ) and total noise (TN) at a targeting bit error rate (BER) level. We illustrate the accuracy improvements with this new method over the conventional methods that do not take BGJ or BGN into account.