Although the bankruptcy would be registered against you, credit files also show information about other members of your family who live at the same address (they simply take this as being anyone living at the same address with the same surname).
So although your wife would not be listed as bankrupt, your bankruptcy will show on her credit searches (and on your stepson's if he shares your surname). If she applied for credit, it would be up to the individual lenders to make up their own mind about whether that means she would be a greater risk as a borrower, but most will likely take that view.
Credit files are also linked by joint borrowing, so if you and your wife have any joint accounts or cards, that would also link your files together even if you lived separately (perhaps uncommon with husband and wife, but it happens with business partners, for example, who have joint business borrowing but are otherwise not linked).
This would not, however, give anyone a claim over her own assets.