I wish I'd had super understanding parents like some people mentioned!
As for me, who didn't then, and who has no intention of opening up to friends/family/coworkers about this now, being careful is paramount. It would be hard to wet in a bathtub and it be seen as an accident. So NEVERNEVERNEVER do it without double-checking that that door is locked, knowing what you're going to do with the clothes, etc.
With the computer, I got real sneaky. I made a folder, changed its icon to a single-pixel white dot and its name to a space, and put it in a folder no one would ever look at. And by that, I mean I buried it several folders deep in the place where I kept all my cartoon-related stuff, and made sure it was in a place where you'd have to do some serious scrolling to get to it. If my parents suddenly cared about Digimon enough to look through my folders about it (not gonna happen), there'd be no way of finding it except knowing EXACTLY where to click. Needless to say, if your stuff is in list view, that wouldn't work, but thankfully ours wasn't.
I also changed any titles to numbers so if you stumbled on it some other way (say, searching for something else, it comes up in the list) it'd not be anything that'd look suspicious or catch your eye at all. If you're looking for a recipe, tax file, etc. you probably overlook "5.jpg" showing up alongside all the other irrelevant stuff.
Like I said, the best way to deal with getting caught is being super effing serious about not letting it happen in the first place. Think it through. Don't just think about when to wet - that's easy. Think about when to clean up. When will you have time to rinse off those wet clothes, toss 'em in the dryer, and put 'em away? Where will no one look, plus think nothing of it on the off chance that they do?
I suppose if caught yellow-panted, I'd go the 'it was accidental' route. People might laugh, but it beats the risk of changing how a friend or family member sees me, which is what I worry about most if it's discovered. Grit your teeth when someone pokes at you about being the one who held it most of the way home but wet on the way to the bathroom, or drank too much water before going to bed the night before, etc. and remember that it could be worse!
I suppose if I lived with parents and had very little privacy (I had about a... medium level of privacy as a kid.) and absolutely determined to wet, the accidental route would have to suffice. Stress is well known to cause bedwetting, so I'd just do it on the bed, limit it to once or twice a week, and when inevitably caught, shyly admit that I've been wetting the bed a while, ever since (insert the most stressful current/recent thing in your life here.)
And of course, wet whenever you're going to be wet anyway! Rain and mud are both just another word for opportunity. Water balloon fights in the summer were even more fun for me 'cause clothes that are already soaked are perfectly wettable. And you better believe any time I was at the pool, I took the opportunity to consume lots of soda and hold it until I had an accident (I didn't pee in the pool; I got out as soon as it got bad enough that it became hard to hold. A fountain of yellow isn't so easy to explain away, too, so I tried to be out of sight for that. If I couldn't hold it long enough, I'd sit down, either in grass, or if no grass, an existing puddle on the ground, and try to make it look natural, like I just felt like sitting there.)
I really, really envy the people whose parents knew and accepted it. It must have been an interesting conversation when they first discovered it!