It doesn’t affect the score on the judge’s card or change a barrel run time, so naturally many riders don’t devote training time to mounting manners. Until it starts to become a bigger problem. Before things escalate to “Butch Cassidy mount-on-the-fly” style, sneak some mounting block training into each riding session. Training in one area of horsemanship spills into others.

Envision a box around your horse. It starts with having a plan and setting the boundaries. Your horse finds pressure when he steps forward, backward or sideways and freedom within box boundaries. This is rewarding by negative reinforcement: taking away something that the horse dislikes (pressure) in order to reinforce a desired response.

Timing is crucial. Whatever your horse is doing when you release pressure, he’ll be more likely to do again. When the horse moves and you interrupt the process by dropping your foot down, backing away and beginning again you give our horses an untimely reward.
Enlist a ground person. It’s tricky to have the right timing to block your horse’s exit while balancing on one foot. At first, a helper can apply pressure to the reins as your horse attempts to leave. Remind your ground person to avoid hanging on the reins when your horse is standing still. The point is to block, not prevent the horse’s exit.
Keep your reins short, but not tight. You should be able to stop any unauthorized step forward with your left hand. If your reins are loopy, one step becomes three steps by the time you gather up the slack. If your reins are taut, your horse will step out the back door of your imaginary box. Often, rider concentration shifts to fitting their foot into the stirrup and away from the messages sent by their rein hand.
Outside rein shorter. Although some successful trainers prefer the opposite, I’ve found it useful to tip the horse’s head slightly to the right, away from me, to prevent the hip from swinging away from me.
Train in increments. Step up, lean over the saddle , step down. Repeat until the horse is nonchalant, displaying no reaction or attempt to move.
Sit down lightly. Horses are understandably bugged and try to leave when riders drag a foot across their rumps, stick a toe in their sides or land with a crash in the saddle. Try to be graceful.