No problem with using the Bow eye!
Use a short mooring Strop 24" will usually do unless it's a Huge Metal Buoy or you are shareing the Mooring ...when you may want something longer.. with a SS lockable ( threaded cover) Shackle on each end.
The rule is Keep all attachments metal to metal...(it's amazing how soon a Rope will wear through attached to a rusty mooring eye with the movement and Tide! seen someone nearly loose there RIB in the Scillies! ) and you'll be fine.