I am very fond of mouting bicycles this way:
Stand to the left of the bike.
Put the left foot on the left pedal.
Push forward with the right foot to set the bike in motion.
Swing the right leg over the back of the saddle, sitting on it as the move is carried out.
You can see it at 0:51 in this video.
However, Sheldon Brown advises against that technique, which he calls "the cowboy monut":
The cowboy mount places the rider's weight on the bicycle while it is leaning over at a sharp angle. This puts considerable lateral stress on the frame and the wheels. Bicycle wheels, in particular, are not designed to withstand serious sideways stresses, and this poor mounting technique is very hard on your wheels.
I don't have one tenth of Sheldon's expertise on bicycles, but that explanation seems insufficient because
The angle involved in the cowboy mount is nearly perpendicular to the ground (as the video shows).
On curves, bicycles are certainly subject to sharper angles than on the cowboy mount.
Warning against "sideway stresses" sounds insubstantial. I can't imagine anything worse than a unbalance and subsequent fall happening.
Instead, Sheldon advises the rider to start by standing astride the frame. Indeed, this provides the most controlled start, especially in irregular or ascending terrain, but it also takes more time to set off than the cowboy mount.
Assuming regular, flat terrain, are Sheldon Brown's arguments against the cowboy mount solid and thus should the classical mount (or maybe some other mount) be preferred, or is it exaggerated?