They are a gorgeous creamy beige colour. The little lambs website isn't very clear as some pictures show them white for some reason - but look at the kits www.littlelamb.co.uk/itemdetl.php/itemprcd/Bamboo-Nappy-Kit-40 here and you will see the proper colour. PS They are excellent nappies and SO FLUFFY I want to wear one....
Cotton has a long pile on them and feel rougher. Bamboo has longish pile too though, but they are definitely not white and I wouldn't call them course to touch at all - they are incrediblt fluffy. (Although the company are v. helpful so maybe call them and ask if they ever were white, if you can think of a way around admitting you didn't buy from them!).
The cotton also feel slightly rougher to the touch, although if you haven't got anything to compare them to I realise that's not much help....!
One thing I forgot to say - you can buy a sample nappy from Little Lambs for £9.50 plus P+P - you get a wrap with it too so you can use it straight away.
I don't know it you might want to buy a single sample from them (get the bamboo one!!) to try out? You can get a sample of each fabric and they will all come with a wrap. This might be useful if you end up having to buy them new after all!
They do sometimes do free nappy offers (Just pay £1.62 for postage) as well, but it's not on there at the moment.
Good luck (with this and with your new arrival....)