Is it possible to send funds from a bitcoin account via routing number to a trading account?
Not without an intermediary. Banks deal with traditional currencies like Euros or US Dollars, whereas Bitcoin is completely based on transactions involving bitcoins.
The only reason bitcoins have a value denominated in USD or Euros is that there are people willing to buy them for that value. Other than that bitcoins and traditional currencies are completely detached from each other.
So either your bank accepts bitcoins and allows you to trade them or, more likely, you'll have to find someone who buys bitcoins and then you transfer the money you received in exchange to your bank account.