yeah , i think you answered your own question , you got a result with sodium bicarb . And you did little damage,
There was probably no better solution for that situation. You have to play around with a few options and see what works .
I had to try and get red berry staining out of a beige linen /cotton bedroom chair this week . I knew if it touched with sod met or oxidiser products there would be glaring white patches when dry . Sodium bicarb was less damaging option and i alternated it with dabs of citric acid ( oust descaler is a good source in the supermarket ) and rinsing with extractor . Actually putting one (citric acid ) on top of the other (bicarb ) fizzes up , im pretty sure that the chem dry carbonation ingredients, any way got there in the end , beige dye intact .