You can visit Vitoria-Gasteiz coming from Bilbao Airport (Loiu) on a toll road or using public transport (Autobuses La Unión). Vitoria-Gasteiz has a small Airport (Aeropuerto de Foronda) 8 km north of the town with a few flight destinations.
Currently the air fares are very low. There is a shuttle bus between the airport and the bus station in the centre of town, which seems timed to coincide with the major arrivals and departures, and cost €3 each way.
There is a left-luggage facility at the Coach Station (to the east of the city centre). Cost is roughly €1 per bag per day, and you can leave luggage for several days