Greetings Anne,
I'm sorry to hear you're having a hard time finding
B&Bs in the cities of Dublin, Cork, and Galway. It's great that you've already checked B&B Ireland. It's what I would have done as well.
Tourism Ireland has an
accommodation search tool that might give you different results than B&B Ireland.
Alternatively, you might want to look for small boutique hotels or guesthouses in city centres. They often offer a similar experience to B&Bs. You could also widen your search area for B&Bs and make sure to find ones that are accessible by
public transport.
I hope this helps! Feel free to reply if you need more help!
Noortje