I'd like to approach this from two angles.
First, why would we want to be tied up in public anyway?
Of course, because it feels good to be tied up, hugged by the ropes, we all know this. But why in public?
Some might have no opportunity to do it at home; no partner, and they're scared of risky self-bondage. And if they are tied up by somebody they just met on the internet, it's safer in a public place than being alone with him.
Others might want to send a statement, a bit like with a punk or gothic outfit: Look at me, I exist, I'm kinky and quirky, and I'm okay like this! And perhaps help normalize it, so people learn that bondage can be fun.
Or it could be an icebreaker, you immediately have a topic to talk about with strangers. And perhaps you might meet a like-minded person?
Then, practical reasons. It stops me from touching my face all the time.
Can you think of more good reasons?
Now second angle, let's take a minute to think about the thoughts and feelings of those who might object to public bondage.
First: "We don't want any crazy perverts here!"
Yes, therefore do it in Berlin,
Amsterdam or Portland, and not in Karenville. And try to avoid sexual connotations. No skimpy or fetishy clothing, no submissive behaviour, make the bondage as casual as possible.
Second: "Think of the children!"
Yes, best would be to pick a place where there are no or very few children around. But if there are, sure, you don't want to traumatize them. Therefore make it light-hearted, chipper and simply normal.
Children might be curious and unafraid to ask simple questions like "why are you tied up?" Have a good response at hand, explain it's just a little fun, or that you've lost a bet. Not sure if you want to describe why it makes you feel good. Don't be creepy!
Third: "You will trip and fall!"
Yes, if you visit a museum with your hands tied behind your back, they might worry that you fall headfirst onto some priceless piece of art and make it all bloody. Not every artist will see that as an improvement.
And if you live in a country where a visit to the emergency room will cost you a lot of money, they'll worry you might try to sue them for compensation. Same as with "Stella vs McDonald's"; people mocked her a lot, but in fact she only sued because of her five-figure medical bills. Therefore, a museum guard might not accept bondage on their premises because they could get into trouble.
Therefore, no alcohol, no other things that might increase this risk. Wear a shirt that says "I'm a big boy and can look after myself", sign a liability waiver, get a proper health insurance, or well, accept that this place is not appropriate for tied people.
Perhaps start with something very harmless. Put your hands into a hair bobble behind your back. If somebody objects, you can pull them out immediately. And explain that you have this bad habit of picking your nose,
biting your nails, or an eye or ear infection, and this is a way to keep you from scratching it all the time.
Try this a couple of times and see what happens. If nothing bad happens, would you dare to hide a cable tie underneath the hair bobble? Such that secretly, you cannot pull the hands out anymore??