We don't offers degrees by that name in the US. In the UK and some other countries, a "professional bachelor's" would be something like a bachelor's of law or medicine. In the US, those are graduate-level degrees, earned AFTER you earn the bachelor's.
It is possible to earn a bachelor's in a field like engineering or accounting in the US, and these would allow you to go straight into a job in those fields. You could call those "professional bachelors"
An academic bachelor's would be a bachelor's in a standard academic subject -- English, History, Chemistry, Biology, etc.