The Vallejo ferry link to check schedules: http://baylinkferry.com/
The airport is about 13 miles south of downtown. Here is one website that gives options on how to reach downtown.
I don't think you would want to bicycle downtown due to traffic but the BART train is a good option. You may want to put together your bicycle and take it onto BART. Here is info about bikes on BART:
The airport has several bike assembly stations:
Hope these links help.