Yes, it's exhilarating making music with others. I'm glad to hear you can make music with others, there's no greater feeling than that, in my opinion.Well, nobody read it - or nobody had any advice.
Happily, it wasn't needed. I've been to two of my fiddle teacher's pub sessions and I found I didn't feel nervous and was able to join in a number of the tunes. My main tip for success is 'lower the bar' - I went with the intention of 'just being there' and listening, and said to myself that if I could join in two tunes, it would be enough. But I managed 11 the first time and 38 the second. It also helped that I felt part of a team, as some players from my other pub session were there and I didn't want them to be left out so kept suggesting tunes that they could lead, and when they did so, I supported them.
It was an exhilarating experience not to be nervous for once!
I don't have any answers to the original question, which is the best teaching method. Depends on the student, depends on the teacher, depends on what you want, depends on age, depends on ability, depends on physical limitations.
As for confidence, its sounds like you gained some confidence making music with others. All performers have some level of anxiety before and during a performance. But in many cases, the audience is forgiving and just appreciates the music. I guess if the audience paid a lot for a performance they might have high expectations, but if the price of admission is the price of a beer in a pub, the audience will love almost whatever you do.