If you're nervous, start by proving to yourself that the risk is tiny.
1. Choose a decent diaper that you are comfortable wearing in public. Maybe not the very thickest, say a high-end medical plastic-backed option like the Tena Active Fit Maxi.
2. Practice using it at home. Experiment with fit and anything you want to wear over it. Try standing, sitting, walking, with different kinds of wettings from little trickles up to major floods.
3. Discover the limits of its performance, e.g. you might find it never leaks even when emptying a full bladder standing up, occasional minor leaks when flooding sitting down, fine with smaller wettings sitting down.
4. Now try it in public, but don't go close to the performance limits you have already found out. E.g, try not to empty a completely full bladder when standing, or avoid wetting more than a little at a time when sitting.
5. The risk is now so small, you can forget about it and enjoy the convenience of never having to find a bathroom.
6. As you build up more experience and confidence, you can push it a little further.
It's easy once you get the hang of it. I can empty my bladder while having a 1:1 conversation and not skip a beat. I often wear plastic pants as a secondary line of defence in critical situations although they are not truly necessary. I can wet just as easily and spontaneously when not wearing them, but the risk of the unexpected, such as a pinhole leak, is technically greater. If you follow the preparation routine I describe and wear good waterproof pants too, you really will have nothing to worry about. Have fun!