Recently saw someone trying to learn this trick. This is one of the tricks I managed to self-learned. So, I would just like to briefly share my experience.
Reason for learning this skill is because I am short, but using an old hybrid 26" bike. Thus, the mounting and dismounting is inconvenient and time consuming. Seeing how most old uncles do it gracefully on their Flying Pigeon like 28 or 29 inch bikes inspire me to acquire this skill.
Initially I tried to learn the mounting. I guess this is the very natural and intuitive approach, since mounting comes before dismounting. However, after many attempts without much progress, I started thinking, maybe I should learn the dismounting first. So true, I managed to dismount while the bike is rolling soon enough. After that, it didn't take long for me to pick up the mounting skill.
The logic is quite obvious. For mounting, one needs to balance a slow moving bicycle while standing on one of the pedal and trying to cross over to seat on the saddle. Trying to execute a couple of new moves at the same time is not helpful. However, for dismounting, one starts off riding the bicycle, then start to try out each of the following steps a little by a little: