I have had a look through the code that I can see that would be linked to displaying this but have not had any luck.
We have some bundled products, of which you can change accessories (i.e. colour/plugs) which have a price of £0.00 (have managed to remove this from the actual product page). However on the shopping basket they show, is there anyway to just remove or hide the price. See image for a clearer understanding:
Assuming that you want to remove it from all items regardless of the price, then you could add this css
#shopping-cart-table dd span.price{
display:none;
}
If you only want to remove the price if it is zero, the you could take a look at /app/design/frontend/default/{theme path}/template/checkout/cart/item/default.phtml (around line # 46)
or
str_replace("£0.00", "", $_formatedOptionValue['value'])
on the string that display that line (make sure to add the currency sign so that £10.00 dont get replace)