https://www.frenchairportguide.com/pis/poitiers-airport-buses.htm says that there are buses directly from the airport to the station, which are timed to connect with the Ryanair flights. It says tickets are €5 from the driver:
The Poitiers Airport buses operate at times which correspond to the Ryanair flight schedules of the airport, and are available from the bus station outside of the arrival area.
Arriving passengers will easily find the bus stop outside of the airport building, and the airport buses depart approximately half an hour after each Ryanair flight arrival. On this bus, passengers can travel to the railway station in the city of Poitiers, from where further bus connections are available, or from where passengers can continue their journey by train.
From Google Streetview, you can walk to the airport from the nearby bus stops for buses from Google Maps but I would only want to do that with a backpack and not a wheeled suitcase. There is a footpath by most of the roads, but sometimes it has a loose asphalt surface and other times it looks overgrown.
Personally, I would get a bus from near the station and walk to the airport, as you can be pretty sure that you are in the right place, and there will be people who you can ask. To get from the airport to to the station, I would either walk all the way, or get a taxi. I don't like waiting at bus stops in the middle of nowhere, unless there is a frequent service or live tracking on an app to tell me that the bus is going to come.
