Hi Haruna,
It's good that you are planning a trip to Ireland. From my experience of
travelling by bus in Ireland, including with Bus Eireann and Aircoach, generally larger bags must be places in the luggage compartment.
For example, Bus Eireann states this
on their website. Only hand luggage, something that is capable of being stored in the overhead rack or beneath the seat, is allowed onto the bus itself. This is done in order to ensure the comfort of all passengers.
The website also states that "personal effects or items of luggage of a relatively expensive nature should not be packed in luggage placed in the luggage compartment, but should be kept in a passenger's hand luggage or on the person of that passenger. Bus Éireann will not be liable for any loss of or damage to such articles if placed in the luggage compartment."
If you are worried about your luggage being taken by another passenger by mistake, perhaps you could make it look distinctive by choosing a colourful bag or tying something distinctive to the outside. I, personally, have never experienced or heard of luggage being taken by another passenger while travelling in Ireland.
Also, in my experience, drivers do not attach a luggage tag to items that are placed in the luggage compartment.
I hope this information will be helpful to you and perhaps other members of the community can offer their advise, too.
Regards,
Eoin