This is not an experience I remember but it sounds exactly like what my son went through when he first got a kilt. He was very excited to get it, but then once he did he was hesitant to wear it. So my advice to you will be pretty much what I did with him. Now my problem is keeping him out of his kilt

Start at a kilt friendly event if possible. Highland games, Burns Supper, a Rabble Kilt Night etc. That is the best place to gain confidence. Once you feel comfortable in that setting then as suggested above go out with a group of friends who know you will be kilted. Once you are comfortable with that you should be fine.

One thing you didn't mention is what kind of kit you have. In other words what type of kilt and whether you have accessories, a jacket etc. The reason I bring this up is I think facing the non kilt wearing public is a tough thing to do for first timers. However I think you are more likely to have a positive experience if you come close to matching their idea of what someone in a kilt should look like.

Yes I know there are members who say, "to h*ll with what anyone else thinks". Fine but most of us do care if only a little. The public has a much narrower view of what a kilt is that most people here so being dressed well is more likley to get you good reviews. Looking well is also a confidence booster and your confidence will show. That will also improve how people react to you.

Now dressing well does not mean wearing a PC to a pub crawl (unless the crawl is after a black tie) but smart casual is a good aim. You will feel good and look good. If you want good examples of smart casual with a kilt I will point you in the direction of pictures posted by Panache and Hamish. If you take notes from their choices I think you will feel great and look great as well and it is likely you will be very well received.

If your goal is ultimately wear your kilt very casually you can always get more casual as you get more comfortable.