Well she will almost certainly be right in saying that all her friends have an account with Bebo, it is very popular with that age group, unfortunately there has been a lot of incidents of paedophilia on Bebo, including a couple of murders I think.
I think the way I would react with this, is to permit her to use it on the condition you can view her account at anytime and inspect it at will or no deal. This is when it is a good idea to have the PC in the Lounge or a non private area.