A bicycle headset structure is provided to aid in concealment of wiring from components mounted in the handlebar area to components mounted on the rest of the bicycle. The bicycle headset structure basically comprises a handlebar attachment member and a tubular spacer member. The handlebar attachment member has wiring passage extends between the handlebar mounting portion and the steerer tube attachment portion. The tubular spacer member has a wiring channel extending between first and second ends of the tubular spacer member and an axial passageway extending axially between the upper and lower end openings of the tubular spacer member. The axial passageway is dimensioned to receive the bicycle steerer tube. The wiring channel is arranged to communicate with the wiring passage of handlebar attachment member when the handlebar attachment member and the tubular spacer member are attached to the bicycle steerer tube.