Alcott never actually reveals Professor's Bhaer exact age; when Jo first describes him, she says he is "most forty" (almost forty), so he is likely a middle-aged gentleman around thirty-five to forty years old. At the beginning of the novel, Jo is only fifteen, and when she travels to New York and meets Fritz, she's around eighteen to twenty. During her stay in New York, Jo and Fritz begin to spend more and more time with each other he becomes romantically interested in her, though she is apparently oblivious. A few years later, when she's nearly twenty-five, Fritz proposes to her and she agrees to marry him; since Jo is almost twenty-five, we can surmise that Fritz is forty to forty-five years old, which would make him fifteen to twenty years older than her.
Jo isn't really concerned with the age difference between the two, however, and she gradually falls in love with him. She doesn't find him particularly handsome or well-mannered, but she likes the fact the he's kind and caring and that she feels safe with him; she also enjoys their conversations, as they have similar views and opinions. In fact, after they marry, they decide to open a boarding school for boys, in which both Jo and Bhaer put their literary knowledge and skills to use. Alcott implies that they have a stable and loving marriage despite their age difference.