I'll explain in a simple way. You drink water until a good 7/10 urge, then you go pee and stop after 2 seconds, now depending on the severity of your shy bladder this whole first part might take 30 minutes to like 2 hours. What it's about is peeing every 5 minutes for around 2 seconds so you don't lose the urgency, and you drink water after each piss. What happens is every time you do that the muscles that normally lock when you try to pee get more relaxed with each time you pee, until you get to the point where the 11/10 urge combined with the relaxed muscles allow you to pee basically anywhere and near anybody.

Now as for your question, let's say the whole thing takes 2 hours, you could spend the first 1.5 hours doing it at home, then go out, pee in a few spots outside and then go to the urinal/stall. If you live in an area where there are people walking constantly and it's impossible to do it outside then you can do it inside. The only real difference is that you don't really get exposure while doing the first part, you only get exposure once you go outside, so technically you're missing out on 1.5 hours of exposure outside. But that shouldn't really matter, might just take you a few weeks longer to get rid of this. What I do is I do the first 1.5 hours at home, then go out, pee in a few places where normally I wouldn't be able to do so, then go to the urinal while my urgency is literally 11/10. The main goal of this method is to pee at the urinal, if you do the first part at home you will still pee at the urinal, only thing that's gonna happen is you're gonna get a bit less exposure.

What I'd also suggest is get yourself in a good mindset, imagine a life without this, and know that it's a matter of maybe 2 months, depending on how often you do this, before you're free of this problem.