After brief research, train to Asheville I couldn't get there from here. Bus would not be impossible (but difficult) and I would not recommend it for you and daughter.
That said, if you are not opposed to flying, there are direct flights from Sanford to Asheville at reasonable prices. You could drive it in one day---about 9 hours or so. If you are a AAA member, they could help. Good luck. We have been to the Biltmore and it's a great place to visit.
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Most people are as happy as they make up their mind to be. Abraham Lincoln
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