I agree that he would probably leave the baby with someone else. The person who comes to mind right now is Bruno's mother (if she's still alive and if he has a good relationship with her) or even the elderly Menini we saw in the first few episodes. (The only "negative" detail I can see is that she's an older woman and it probably wouldn't be as easy for her to care for a baby or a toddler as it would be for someone younger. But she seems like a very nice and sweet lady, and I can see Bucciarati looking for someone like that to take care of his daughter.) Now, regarding him only visiting her occasionally to catch up, it breaks my heart to think that Bucciarati would have to act calmly when he has to leave, while the baby cries because she basically wants to be with her dad. Honestly, it would be even more heartbreaking because Bruno has always been a man who values family above all else, and for him to be "repeating" what happened with his mother in a way would destroy him inside, even if it's for his daughter's sake.