Rob, part of the time I am the same way - if I am distracted and build up more urine in my bladder than I intend, then after I get up it sort of "hits" me and I have to rush to the toilet. Some times I do not make it in time and it just starts on its own.

Other times, as I get up, it is so obvious that I will not make it in time that I just stop fighting it and let myself go in the diaper. Less frequently I will find myself peeing while I am sitting at my computer working. That is puzzling as I probably could not voluntarily pee while sitting if you put a gun to my head!
During the mornings, after my preventive enema I can expect to be safe from bowel accidents. During that period I try to exercise my urinary control by wearing only a pull-up, with no plastic pants, compression pants, or onesies, so that I can make it to the toilet and be ready to pee quickly. Even so, I do not make it about 1/3 to 1/4 of the time.
Rob, I have ramped up my Kegel exercises as I had some indications that I needed to do so to strengthen my pelvic floor some more. As the exercises can be somewhat tedious - let's be frank, BORING, I have some apps on my iPhone for various routines of Kegel exercises. That breaks up the monotony and encourages me to work out a little more than I otherwise might. I probably do that 4 days a week. On the other days my exercises are informal - while washing dishes, walking around, driving the car, or watching television. The details of the length of the Kegel and the exact number probably are much less than just trying to do as much as you comfortably can fit into your lifestyle.
As I indicated in another message, I will be asking my doctors about the value of pelvic floor exercisers with bio-feedback for home use or some more formal bio-feedback therapy. At this stage I am not sure what my insurance will cover as I had that about two years ago for bowel incontinence. Perhaps if it is justified this time as for urinary incontinence it will go through.
--John