Do you mean the ride will take place from May to September or happen sometime in between those months?
A good place to start would be at your local bike shops, hang out, get to know people in the scene so to speak. Join some local weekly group rides which are done by most bike shops and make some friends. You may also ask the local shops if they have somewhere they would let you hang a flyer or set a stack of them by the register. A couple shops by me have a cork board they will let you hang business cards or flyers on for example.
The issue here is a ride of that magnitude is not just a weekend kind of thing, people will need to make plans ahead of time, take off work, pontentially buy touring gear or any number of other things. Cross country trips take careful planning and execution.
In my opinion one of the best routes will to be to ride with as many people ahead of time so you can to ask around for people that would be interested and get to know the locals that are into this sort of thing. You could also join your local cycling groups on Facebook and start spreading the word and gauging interest through them. One more option would be to take out a classified through either an advocacy group, online, or in a local newspaper if you want to go really old school. With today's technology Facebook may be one of the easier ways to begin. Meet some people interested and take a couple group rides with them before hand to see if you mesh.