Which Liverpool Premier Inn is closest to the cruise terminal please?
I'm not sure if this is the nearest, but it took no longer than 15-20mins to travel on the bus from a stop very close to this Premier Inn to the city centre.
May I suggest you contact the Premier Inn Hotel Reception directly, they were very helpful with which buses to use on our stay. I am sure they would be able to give you details of services available, and if there was a Premier Inn nearer or more suitable for your needs.
I hope this answer might point you in right direction.
Get an answer from Premier Inn Liverpool (West Derby) Hotel staff and past guests.