I don't know anything about Bancroft's, but am applying for my child to attend Forest in September 2008. Forest set their own exams, (as Im' sure Bancrofts also do), which are different from the 11+. Instead of the 11+ verbal and non-verbal reasoning, there's a more traditional maths paper and English paper. Both are on the same day, which is Saturday 26th January. You will get one sample paper from the school in their admissions pack. I think that scholarships are awarded purely on on academic merit (based on your child's exam results), but they do have some bursaries where family income is under a certain amount (I think Â£37k), and I don't know how they assess these. You can find out more on their website, www.forest.org.uk
As for tutoring, everyone has their own opinion. I've had my child tutored for the 11+ since last January and I think that at least a couple of months would be needed to familiarise the child with the papers. At 10, they have no experience of sitting formal exams. However, if you have the time (and energy!) and the right kind of relationship with your child, you could certainly do the coaching yourself. Hope this helps.