What did the Ladybird offer to do for James to help him during their journey and why?

From the text:

‘At this moment,’ continued the Ladybird, ‘our Centipede, who has a pair of jaws as sharp as razors, is up there on top of the peach nibbling away at that stem. In fact, he must be nearly through it, as you can tell from the way we’re lurching about. Would you like me to take you under my wing so that you won’t fall over when we start rolling?’