I'd go with Owen's advice, a single coat of something clear, doesn't really matter what, between the two colours should solve your problems.
Also always spray the lightest colour first, in this case the white, then you do not need to be so heavy with the darker coats to cover the first colour, this should help with any bleeding through.
Also always spray the lightest colour first, in this case the white, then you do not need to be so heavy with the darker coats to cover the first colour, this should help with any bleeding through.