Is there any way I can salvage a dress with localised colour run?

[BabyRuSh]

We bought dd a lovely handmade dress while on holiday. It's cream with two rows of about 5 embroidered flowers. The red thread from one flower on each row has run slightly into the cream material. Is there anything I can do to fix this?? I was really hoping to keep it for potential future dc, but am a bit anal about stains/ colour runs! Please tell me there is a magical rescue for this dress. Tia!

As a really extreme last resort could you try dabbing the red 'runs' with a cotton bud dipped in bleach? I did this with a dress of dd's last year that had gone to mildew after dh left it damp in a beach bag (where it lay, undiscovered, for nearly a fortnight )

It worked, and didn't disintegrate, as I had half expected, but I was pretty painstaking and used the bleach sparingly

Colour run remover stuff from the supermarket, then iron the embroidery as hot as the dress will take (assuming it's normal cotton embroidery thread). Heat may not help, but it fixes silk paint and screen printing dye and is worth a try.