Does a scale model with 1/2 the linear length have 1/8 the mass? If a scale model has 0.5x the original length in all directions, should its mass be 1/8th of the original mass?
 A: Yes, assuming it has the same density. Volme scales as length to the power of three and mass is proportional to volume.
$$
\left(\frac{1}{2}\right)^3=\frac{1}{8}
$$
A: OK, now we have a better idea what you're trying to do.  If we can assume elastic collisions, then answer should be independent of the mass of the bike (though it will depend on the relative distribution of the mass, i.e. center of gravity and moments of inertia).  However you will need to think how to scale the velocity of your model.
One way to think of it:   you want to make a coordinate transformation from your model system that replicates the physics of your target system.  The length transformation from model to target system is $l_t = 2*l_m$.   However, your model system has a gravitational acceleration of $g = 9.8 m/s^2$, so your simulated target system will have an effective gravitational acceleration of $g_t = 2*9.8 m/s^2$ which is not right.  How do you fix this?  You have to rescale the time between model and target systems:   $t_t = \sqrt2*t_m$.  This in turn means your models velocity will be related to the target system velocity by $v_m = l_m/t_m = (\sqrt2/2)*l_t/t_t=v_t/\sqrt2$, so you will want to reduce the velocity of your model accordingly.
