Lifelong a couple of suggestions. I buy completely plain white.Sainsbury's for packs of 10 for about £5, but these are really plain, and I find a bit low in the keg. Tesco do some really nice ones, about £5 for 5 pairs, again, very simple, but with a nicely lace waistband. I think these would go below the skirt of the tutu, although for DD2 (6) I coukd see them on her, not helped by the fact they had to wear white tights and she us very olive skinned. M&S do a version too, but more expensive.
One alternative is to dye white ones with tea, so they go beige. To do this I stuck 2 teabags into a jug, let it go really stewed, then stuck the pants in until the tea was cold.
Final suggestion, you coukd try a pair of size 6 flesh coloured no seam knickers from Debenhams. I tried these a couple of years ago on DD1 but they were too big. Depends on how big your 11 year old is. I could try them on my 10 year old later when she gets back from Granny's house.
Our dancing teacher insists on plain white, then we spend all Showtime telling the little girls to tuck their pants in because they are showing!