I know that bicyclists use the road shoulders to ride across the Antioch Bridge. Do cyclists ride through the toll plaza in the same lanes as motor vehicles? Do cyclists have to pay the toll?

Nope - you cross the toll entrance in the bike lane (right shoulder), and do not pay any toll.

Are you sure about no toll? I have a vague, though perhaps inaccurate, memory of having o pay something silly like 10 cents or something.

Does the bike lane/right shoulder go through the booth, or around it?

I checked the Caltrans site for the bridge and there is no toll for bikes. If I read the site correctly even pedestrians can walk across the bridge. Ariel photos make it look like you can ride past the toll booth on the east-right-hand side northbound.

I've ridden the Antioch bridge twice this summer. No toll + okay shoulder.

Notice the sign on the right "Permitting" bicycles.

I've ridden the Antioch bridge twice this summer. No toll + okay shoulder.

Notice the sign on the right "Permitting" bicycles.

Yup. Just be careful coming off the Delta side. As I recall, there is a fairly significant lip where the bridges joins the roadway at the end, and it could easily give you an instant pinch-flat.