Ladybirds are unlikely to bite you, although they can give you a gentle pinch if they accidentally mistake you for a greenfly.
If you pick up a Ladybird, it might release a yellow fluid that is pungent and slightly caustic. This is actually blood which comes out of its body at the joints on its legs. It has a very bad taste and once a bird has sampled this it will be unlikely to eat another ladybird.
Ladybirds don't sting. Their bright colours are a warning to other animals that they taste bad. In fact they have very few natural enemies.