Hi Stuart! Thanks for your message. It's great to hear you're thinking of travelling to the island with your 91-year-old mum!
For travel between the UK and Ireland, your mum, in principle, does not need a passport as long as she is a British citizen. However, in practice, airlines almost always require a valid passport, and while ferry operators may be more flexible, they will still require government-issued photo ID. Unfortunately, a bus pass is unlikely to be accepted. I would still recommend checking directly with the airline or ferry company you plan to use before you travel to see what's acceptable.
You can find additional details about travel documents and requirements
here.
Let me know if you have any other questions, and eventually, if you need any travel ideas!
Alex