If we take the current speed record of 189.3mph as a max speed on Earth to model from:
Aerodynamic resistance should be the same as drafting behind a canopy (as in the earth speed record attempt) considering there is no atmosphere on the moon.
Gravitational pull/downward frictional resistance is 1/6th. If there is a linear relation (?) and all things being equal, one should travel six times faster in 1/6 gravity.
so I'll say a base figure of 6x183.9 or 1103.4 mph.
That assumes sufficient staggered gearing and run on distance to ramp up to that speed and a human with enough physical capacity to maintain a constant RPM until you get there.
I think however, there will be a reduction in that speed estimate due to frictional losses from the bikes components themselves.