What you're describing is functionally
exactly the same as civil forfeiture that everyone is complaining about!
Civil forfeiture works fine for this case, which is the whole point, because indeed neither will Bob be able to demonstrate it's really his, nor will Alice be arriving to collect.
Where it all goes wrong in other cases is "Bob claim it's his and applies for a writ". i.e. it becomes Bob's responsibility to prove his ownership in court, rather than the government's job to prove anything at all.
i.e. the government performs an administrative seizure without any proof obligation, and then reverses the burden of proof onto the person from whom the assets were seized
In the real world, for small-time asset forfeiture, the amount involved is too small to be worth the effort; or Bob often doesn't have the money for a lawyer to bring that action; or this all happens while he's traveling away from home, so the court appearances are going to involve air fare, time off work etc. Or Bob is presented with the problem of proving something that is difficult to evidence, like "I have been saving this shoebox full of cash in the closet for a long time for my daughter's quinceañera"[1].
Ultimately, yes, due process is available but it's not free, it's not low-friction, and it's many a time not worth it.
[1] https://thehill.com/opinion/criminal-justice/578798-the-high...