We're applying only in my husband's name and his was around 670 when we got preapproved. With a BK and/or foreclosure, you definitely want to be over 620 and 660 or higher will get you a much smoother ride.
Definitely get rid of the CA before you do anything.
Borrowers without a BK/F and with a score below 620 may be able to get a loan if everything else looks good. It seems like pretty much all USDA is manually underwritten and while they have guidelines they are encouraged to bend them if there are mitigating factors. Like any lender though, they want to be comfortable you'll be able to pay the loan so if you have a BK with more recent blemishes you'll have a tougher time.