Besides going on walks or doing ground work, I've often bitted ours while they are eating. It works well for me - I'm in the general area if they get into trouble and can check on them in between feeding each "batch" of ponies.
Wizard
Oly - you can see he's rubbed the browband up over his right ear here (he rubs his head a lot and you now have to watch him when he's standing still in harness).
It's funny how your bit collection will grow. I even have two that I made - when a couple ponies weren't doing well with a mullen or a french link or a dog bone... They work similar to the leather bit and I drove the one mare that way for months (before I decided she and I just weren't going to work as a driving partnership - single or paired). It did actually help - she seemed to have one less thing that she fussed about while hitched.
I've never had the opportunity to try a Myler bit and the Kelly's that are "knock-offs" of them are very thick in the mouthpiece so I haven't tried them either. I find that ours seem to prefer the much smaller diameter mouthpieces - their mouths stay closed UNLESS they are actually resisting or the hands have gotten too rough.
Length of time? Put it on the first time while you're grooming her. Keep it on her while you take her for a short walk. Then remove it, praising her while you you either groom her again or turn her loose. OR put it on while she's eating and remove it when she's done eating - time can vary.