Not from San Jose. The Airport shuttle bus number 10 runs from Santa Clara station to the San Jose Airport.
From Diridon, you could take the 902 light rail towards Mountain View disembark at the Metro/Airport stop then board the Airport shuttle. To add to Brittana 365's response that airport shuttle bus from the Santa Clara Station is operated by the Valley Transportation Authority (VTA) and it's currently free.
Stop by the station for clarification & alternative transportation. Nice folks to assist w/questions.
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