It's 2200 miles or so so that means a month of riding at 65 miles a day. Warmshowers.org will help on accommodations as long as you're willing host too when you're settled. This is the wrong time of year to do this ride! You can head straight south and go across the southern US, but that adds even more miles. Now you're at 2700 miles to stay warm! You have to budget for food in there and even cooking all your own oatmeal and beans and rice, it adds up. All that to say, you're not getting there by bicycle by the 18th of October.