I'm a reasonably good reader, but a bad rememberer. Not that I don't know the tunes, but as someone once said to me at an Irish fiddle festival, "I know what you mean. I can play anything so long as someone remembers it for me"
And if you play an Irish (or English or anything else) tune not in the same way as the rest of the players in the session you will get some funny looks!

Jack, those renderings of the allemande are as beautiful as they are different. But could you dance to them? They are after all baroque, not romantic, and from what are basically dance suites. Art music tradition was well distorted by victorian "correctness".
One hope I had as a newcomer to "folk" many years ago was that it would shed some light on how the music of Bach and earlier composers should be played. I discovered that there was not even a concensus of how "folk" should be played (not necessarily a bad thing!).

But as to the thread, I struggle through constant repetion of each phrase, initially from the dots, then putting them away until I get stuck. In a session of course you don't have to remember, you just "read" what the others are playing (look at fingers, listen hard); and hopefully the tune will eventually embed itself in the brain, so you can play it solo. Singing and improvising on your instrument are a help (as John in kansas suggested). And it's a great help as well if your instrument is tuned to the others you're playing with and not one of those silly black....but that's off thread I think!