I´ve heard from several Doms/Dommes that they sometimes find it difficult to take their sub out with a leash. It draws attention to you and your sub and it´s often not positive attention, but for the Doms/Dommes and of course subs that don´t like that type of attention it can be difficult to use a leash outside. A collar can be hidden, depending on what type of collar, but when you take your sub out with a leash then people can clearly see what you´re doing. So don´t be suprised if judgement and stares come along with that, which makes it not something for everyone.
I think it goes without saying but the opinions of strangers don´t really matter, because if you and your sub are having a good time doing what you do then who cares what other people think! Of course that´s easily said than done, which means that outside you might feel uncomfortable using a leash on your sub and maybe your sub isn´t that comfortable with that either. So does that mean that you stay inside? Some people keep their fetish lifestyle a secret from others, it´s all behind locked doors and that´s quite alright. Personally I find that a shame though, because sometimes I do feel like I´m the only one who´s interested in a kinky lifestyle. Because so many people walk around in their casual clothes and not their fetish clothes, which once again makes sense but it´s a shame because it´s a good way to meet people who like the same stuff as you.
How do you go from inside domination to outside domination? Usually with small steps, if you´re uncomfortable with this then you might want to start small instead of going crazy. A collar is a good way to start, but if that´s too much then use body language to make clear who the dominant one is. You walk up front and your sub walks behind you or your sub asks you for permission to do something, these seem like something small but it´s still dominating your sub. At the same time you´re getting slowly comfortable of dominating out in the open, sure it´s not that clear to others as when you walk around with your sub on a leash but I do think it´s a good way to start!
If people do decide to annoy you or taunt you, then it´s best to ignore them. Those that don´t understand you often don´t want to understand you, so anything you say to these people is often a waste of time. Don´t let that ruin your day or what you want to do, because if you want to go out with your sub on a leash then that´s your business and none of theirs!