Yes, every person requires a US passport to go to Tijuana especially on a bus. Unless they have dual citizenship of Mexico. If you dont have a passport Mexican immigration might let you pass but at the end it is up to them. To enter the US you just require a proof of citizenship which is a passport, or birth certificate (if birth certificate you also need a picture Id).
Yes
Yes, and every person should carry a copy of their birth certificate. Birth certificate should be notarized too.
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