What is the best way to transfer a large sum of money from my checking account at scotiabank to my new account at Bank of America?
You didn't specify where in the world you account is - ScotiaBank operates in many countries.
However, for large amounts where there is a currency conversion involved, you are almost guaranteed to be better off going to a specialist currency broker or payments firm, rather than using a direct method with your bank (such as a wire transfer).
Based on my assumption that your account is in Canada, one provider who I have personally used with success in transferwise, but the best place to compare where is the best venue for you is https://www.fxcompared.com
In the off chance that this is an account with Scotiabank in the United States, any domestic payment method such as a domestic wire transfer should do the job perfectly well. The fees don't matter for larger amounts as they are a single fee versus a percentage fee like you see with currency conversions.