Yes, it is possible. Bizform is a form as any other - e.g. the form for a document type, custom table, etc.
To create it, you need to use the DataClassInfo and DataClassInfoProvider classes to create given "class" (in this case the class in CMS_Class table).
I would recommend to watch this webinar
about Kentico Form engine.
Also, you can take inspiration from the UI and the code behind files (how to find a location of a UI file
And this knowledge base
is about cloning a document type - which is basically a creation of new class - so the idea is the same for creating new form too.