Would the density and radius of your metal appear to be higher or lower if you forgot to tap the flask to release air bubbles?
In this experiment, you were determining the average volume that a copper atom occupied in your sample of copper.  In order to do this, you had to know the number of copper atoms and the volume that number of copper atoms occupied.  

The moles of copper was measured by gravimetrically determining the mass of the copper (e.g. by weighing it). From that you determined the number of moles of copper using it's atomic weight, and from there you calculated the number of copper atoms using Avogadro's number.  

The volume occupied by your copper sample was determined by measuring how much water the copper displaced. So, if the volume of water increased by 10 $\mathrm{cm^3}$, then you knew your volume of copper was $\mathrm{cm^3}$. But air bubbles occupy space also.  If, for example, 1 $\mathrm{cm^3}$ of the total displaced volume were actually due to air bubbles, then you would actually only have 9 $\mathrm{cm^3}$ of copper, but you would mistakenly have used a value of 10 $\mathrm{cm^3}$.  

So, the bottom line is that because you were calculating the molecular volume as the volume occupied by the copper per molar quantity of copper, your calculated molar volume would have been proportionally higher than the true value.