Since your date was this weekend, this is too late to help this time around, but something to consider for the future might be nursing pads. They are super thin and soft. I have no idea how they would function in an exercise situation with a lot of sweat, but I used them when I was nursing, not because I had a lot of leaking, but because all the nursing bras were so thin they did not conceal nipples. The nursing pads provided just enough lining to keep things covered.
Hope your date went well!